Wikipedia:WikiProject Mathematics/PlanetMath Exchange/28-XX Measure and integration
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This page provides a list of all articles available at PlanetMath in the following topic:
- 28-XX Measure and integration.
This list will be periodically updated. Each entry in the list has three fields:
- PM : The first field is the link to the PlanetMath article, along with the article's object ID.
- WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
- Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
Status | means PM article |
N | not needed |
A | adequately covered |
C | copied |
M | merged |
NC | needs copying |
NM | needs merging |
- Please update the WP and Status fields as appropriate.
- if the WP field is correct please remove the qualifier "guess".
- If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
- If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
- If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.
Don't forget to include the relevant template if you copy over text or feel like an external link is warranted
- {{planetmath|id=|title=}} for copied over text
- {{planetmath reference|id=|title=}} for an external link
See the main page for examples and usage criteria.
One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.
28-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- PM: Comparison between Lebesgue and Riemann Integration, id=7343 -- WP: Lebesgue integration -- Status:
- PM: bound on error of Simpson's rule, id=7979new! -- WP guess: bound on error of Simpson's rule -- Status:
28-01 Instructional exposition (textbooks, tutorial papers, etc.)
- PM: an integrable function that does not tend to zero, id=9202new! -- WP guess: an integrable function that does not tend to zero -- Status:
28A05 Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets
- PM: Borel \sigma-algebra, id=951 -- WP: Borel sigma-algebra -- Status: A
- On PM they have just a lame definition. Oleg Alexandrov | talk 18:22, 5 Feb 2005 (UTC)
- PM: limit superior of sets, id=3689 -- WP: limit superior of sets -- Status: A
- Made it a redirect to limit superior and limit inferior where this info exists. Oleg Alexandrov (talk) 01:58, 24 October 2005 (UTC)
- PM: measure zero, id=4898 -- WP guess: measure zero -- Status: A
- On PM they just have a lame definition. Oleg Alexandrov | talk 21:19, 5 Feb 2005 (UTC)
- PM: Kolmogorov zero-one law, id=9425new! -- WP guess: Kolmogorov zero-one law -- Status:
- PM: monotone class, id=9426new! -- WP guess: monotone class -- Status:
- PM: monotone class theorem, id=9429new! -- WP guess: monotone class theorem -- Status:
- PM: proof of Vitali's Theorem, id=4467new! -- WP guess: proof of Vitali's Theorem -- Status:
- PM: sequence of sets convergence, id=8358new! -- WP guess: sequence of sets convergence -- Status:
- PM: sigma--ring of sets, id=9369new! -- WP guess: sigma--ring of sets -- Status:
- PM: tail event, id=9424new! -- WP guess: tail event -- Status:
28A10 Real- or complex-valued set functions
- PM: \sigma-finite, id=2723 -- WP: sigma-finite -- Status: A
- Redirects to measure (mathematics) where this definition is stated. Oleg Alexandrov (talk) 08:51, 22 October 2005 (UTC)
- PM: Argand diagram, id=751 -- WP: Argand diagram -- Status: A
- Redirects to complex number, where this info is covered.Oleg Alexandrov (talk) 08:51, 22 October 2005 (UTC)
- PM: Hahn-Kolmogorov theorem, id=5409 -- WP: Hahn-Kolmogorov theorem -- Status: C
- PM: measure, id=756 -- WP: measure (mathematics) -- Status: A
- PM: outer measure, id=4456 -- WP: outer measure -- Status: A
- PM: properties for measure, id=4460 -- WP: measure (mathematics) -- Status: A
28A12 Contents, measures, outer measures, capacities
- PM: absolutely continuous, id=3997 -- WP guess: absolutely continuous -- Status:
- PM: complete measure, id=5520 -- WP: complete measure -- Status: A
- PM: completion of a measure space, id=5521 -- WP: completion of a measure space -- Status: A
- Redirects to measure (mathematics) where this concept is explained. Oleg Alexandrov (talk) 07:18, 24 October 2005 (UTC)
- PM: counting measure, id=2096 -- WP: counting measure -- Status: A
- PM: Hahn decomposition theorem, id=4014 -- WP: Hahn decomposition theorem -- Status: M
- Merged and redirected to signed measure. Oleg Alexandrov (talk) 08:49, 24 October 2005 (UTC)
- PM: Jordan decomposition, id=4015 -- WP: signed measure -- Status: M
- Merged to signed measure. Oleg Alexandrov (talk) 08:49, 24 October 2005 (UTC)
- PM: Lebesgue decomposition theorem, id=4003 -- WP: Lebesgue's decomposition theorem -- Status: C
- PM: Lebesgue outer measure, id=341 -- WP: Outer measure -- Status: A
- We have the fully general defintion in any measure space, not just the real line. Oleg Alexandrov (talk) 19:51, 8 March 2006 (UTC)
- PM: outer regular, id=2938 -- WP: outer regular -- Status: A
- PM: proof that the outer (Lebesgue) measure of an interval is its length, id=6435 -- WP guess: proof that the outer (Lebesgue) measure of an interval is its length -- Status:
- PM: signed measure, id=4013 -- WP: signed measure -- Status: C
- Copied and merged with Hahn decomposition theorem and Jordan decomposition. Oleg Alexandrov (talk) 08:49, 24 October 2005 (UTC)
- PM: singular measure, id=4002 -- WP: singular measure -- Status: C
- PM: support of integrable function with respect to counting measure is countable, id=6698 -- WP guess: support of integrable function with respect to counting measure is countable -- Status:
- PM: Bolyai-Gerwien theorem, id=8720new! -- WP guess: Bolyai-Gerwien theorem -- Status:
- PM: continuous almost everywhere versus equal to a continuous function almost everywhere, id=7996new! -- WP guess: continuous almost everywhere versus equal to a continuous function almost everywhere -- Status:
- PM: quasi-invariant, id=7942new! -- WP guess: quasi-invariant -- Status:
28A15 Abstract differentiation theory, differentiation of set functions
- PM: Hardy-Littlewood maximal operator, id=4024 -- WP guess: Hardy-Littlewood maximal operator -- Status:
- PM: Hardy-Littlewood maximal theorem, id=4025 -- WP guess: Hardy-Littlewood maximal theorem -- Status:
- PM: integral depending on a parameter, id=4517 -- WP guess: integral depending on a parameter -- Status:
- PM: Lebesgue differentiation theorem, id=4026 -- WP guess: Lebesgue differentiation theorem -- Status:
- PM: Radon-Nikodym theorem, id=3998 -- WP: Radon-Nikodym theorem -- Status: M
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
- PM: dominated convergence theorem, id=3677 -- WP: dominated convergence theorem -- Status: A
- PM: Egorov's theorem, id=3699 -- WP: Egorov's theorem -- Status: A
- PM: Fatou's lemma, id=3678 -- WP: Fatou's lemma -- Status: A
- PM: Fatou-Lebesgue theorem, id=3679 -- WP guess: Fatou-Lebesgue theorem -- Status:
- PM: measurable function, id=3176 -- WP: measurable function -- Status: A
- PM: proof of dominated convergence theorem, id=4077 -- WP guess: proof of dominated convergence theorem -- Status:
- PM: proof of dominated convergence theorem, id=6123 -- WP guess: proof of dominated convergence theorem -- Status:
- PM: proof of Egorov's theorem, id=4518 -- WP guess: proof of Egorov's theorem -- Status:
- PM: proof of Fatou's lemma, id=4076 -- WP guess: proof of Fatou's lemma -- Status:
- PM: uniformly integrable, id=7211 -- WP guess: uniformly integrable -- Status:
- PM: almost continuous function, id=8329new! -- WP guess: almost continuous function -- Status:
- PM: criterion for interchanging summation and integration, id=8465new! -- WP guess: criterion for interchanging summation and integration -- Status:
- PM: Lusin's theorem, id=8330new! -- WP guess: Lusin's theorem -- Status:
- PM: modes of convergence of sequences of measurable functions, id=8335new! -- WP guess: modes of convergence of sequences of measurable functions -- Status:
- PM: proof of Fatou-Lebesgue theorem, id=7997new! -- WP guess: proof of Fatou-Lebesgue theorem -- Status:
- PM: regarding the sets A_n from the traveling hump sequence, id=8344new! -- WP guess: regarding the sets A_n from the traveling hump sequence -- Status:
- PM: traveling hump sequence, id=8336new! -- WP guess: traveling hump sequence -- Status:
- PM: Vitali convergence theorem, id=8401new! -- WP guess: Vitali convergence theorem -- Status:
28A25 Integration with respect to measures and other set functions
- PM: L^{\infty}(X, d\mu), id=4797 -- WP guess: L^\infty(X, d\mu) -- Status:
- PM: \mathbb{L}^p vs \mathbb{L}^q, id=7194 -- WP guess: \mathbbL^p vs \mathbbL^q -- Status:
- PM: Clarkson inequality, id=8142new! -- WP guess: Clarkson inequality -- Status:
- PM: proof of Clarkson inequality, id=8562new! -- WP guess: proof of Clarkson inequality -- Status:
28A33 Spaces of measures, convergence of measures
- PM: Koch curve, id=1186 -- WP: Koch curve -- Status: A
- PM: measurable space, id=755 -- WP: measurable space -- Status: A
- PM: weak-* topology of the space of Radon measures, id=7212 -- WP guess: weak-* topology of the space of Radon measures -- Status:
28A35 Measures and integrals in product spaces
- PM: Fubini's theorem for the Lebesgue integral, id=5719 -- WP guess: Fubini's theorem for the Lebesgue integral -- Status:
- PM: product measure, id=952 -- WP: product measure -- Status: C
- PM: Tonelli's theorem, id=5713 -- WP: Tonelli's theorem -- Status: A
- PM: proof of Fubini's theorem for the Lebesgue integral, id=7189 -- WP guess: proof of Fubini's theorem for the Lebesgue integral -- Status:
- PM: infinite product measure, id=8532new! -- WP guess: infinite product measure -- Status:
28A60 Measures on Boolean rings, measure algebras
- PM: \sigma-algebra, id=950 -- WP guess: sigma-algebra -- Status: A
- PM: \sigma-algebra, id=4835 -- WP: sigma-algebra -- Status: A
- PM has two articles on this topic for some reason. Oleg Alexandrov (talk) 14:14, 24 October 2005 (UTC)
- PM: measurable set (for outer measure), id=4458 -- WP guess: measurable set (for outer measure) -- Status:
28A75 Length, area, volume, other geometric measure theory
- PM: example 1 of integration with respect to surface area, id=6664 -- WP guess: example 1 of integration with respect to surface area -- Status:
- PM: example 2 of integration with respect to surface area, id=6665 -- WP guess: example 2 of integration with respect to surface area -- Status:
- PM: example 3 of integration with respect to surface area, id=6666 -- WP guess: example 3 of integration with respect to surface area -- Status:
- PM: example 4 of integration with respect to surface area, id=6667 -- WP guess: example 4 of integration with respect to surface area -- Status:
- PM: example 5 of integration with respect to surface area, id=6668 -- WP guess: example 5 of integration with respect to surface area -- Status:
- PM: example 6 of integration with respect to surface area, id=6669 -- WP guess: example 6 of integration with respect to surface area -- Status:
- PM: example 7 of integration with respect to surface area, id=6672 -- WP guess: example 7 of integration with respect to surface area -- Status:
- PM: example 8 of integration with respect to surface area, id=6673 -- WP guess: example 8 of integration with respect to surface area -- Status:
- PM: integration with respect to surface area, id=6660 -- WP guess: integration with respect to surface area -- Status:
- PM: Lebesgue density theorem, id=3869 -- WP: Lebesgue density theorem -- Status: C
- PM: derivation of first formula for surface integration with respect to area, id=6862 -- WP guess: derivation of first formula for surface integration with respect to area -- Status:
- PM: derivation of second formula for surface integration with respect to area, id=6863 -- WP guess: derivation of second formula for surface integration with respect to area -- Status:
- PM: invariance of formula for surface integration with respect to area under change of variables, id=6865 -- WP guess: invariance of formula for surface integration with respect to area under change of variables -- Status:
28A78 Hausdorff and packing measures
- PM: area formula, id=5979 -- WP guess: area formula -- Status:
- PM: Hausdorff measure, id=5976 -- WP guess: Hausdorff measure -- Status:
28A80 Fractals
- PM: Cantor set, id=2083 -- WP: Cantor set -- Status: NM
- PM discussion of fat Cantor sets needs to be merged or put to fat Cantor set. linas 16:27, 26 August 2006 (UTC)
- PM: Hausdorff dimension, id=2981 -- WP guess: Hausdorff dimension -- Status:
- PM: Menger sponge, id=5968 -- WP: Menger sponge -- Status: A
- PM: Sierpinski gasket, id=3011 -- WP: Sierpinski gasket -- Status: A
- PM: Barnsley fern, id=8154new! -- WP guess: Barnsley fern -- Status:
- PM: closure and interior of Cantor set, id=7671new! -- WP guess: closure and interior of Cantor set -- Status:
- PM: Douady rabbit, id=9602new! -- WP guess: Douady rabbit -- Status:
- PM: Mandelbrot set, id=9237new! -- WP guess: Mandelbrot set -- Status:
- PM: Peano curve, id=8723new! -- WP guess: Peano curve -- Status:
- PM: proof of existence and unicity of self-similar fractals, id=8153new! -- WP guess: proof of existence and unicity of self-similar fractals -- Status:
- PM: quadratic Julia set, id=9574new! -- WP guess: quadratic Julia set -- Status:
- PM: San Marco dragon, id=9603new! -- WP guess: San Marco dragon -- Status:
- PM: self-similar fractals, id=8146new! -- WP guess: self-similar fractals -- Status:
28A99 Miscellaneous
28Axx Classical measure theory
28B05 Vector-valued set functions, measures and integrals
- PM: vector measure, id=9877new! -- WP guess: vector measure -- Status:
28B15 Set functions, measures and integrals with values in ordered spaces
- PM: locally integrable function, id=4430 -- WP: locally integrable function -- Status: C
- PM: fundamental lemma of calculus of variations, id=6745 -- WP: fundamental lemma of calculus of variations -- Status: M
- Copied the references. Oleg Alexandrov (talk) 20:00, 8 March 2006 (UTC)
- PM: example of function not Lebesgue Measurable with measurable level sets, id=7841new! -- WP guess: example of function not Lebesgue Measurable with measurable level sets -- Status:
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections
- PM: Fractional calculus, id=8430new! -- WP guess: Fractional calculus -- Status:
28Bxx Set functions, measures and integrals with values in abstract spaces
28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
- PM: Haar integral, id=4324 -- WP guess: Haar integral -- Status:
- PM: Radon measure, id=7797new! -- WP guess: Radon measure -- Status:
28C10 Set functions and measures on topological groups, Haar measures, invariant measures
- PM: Haar measure, id=2959 -- WP: Haar measure -- Status: A
28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
- PM: Krylov-Bogolubov theorem, id=5525 -- WP guess: Krylov-Bogolubov theorem -- Status:
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
- PM: essential supremum, id=2044 -- WP: essential supremum -- Status: C
28Cxx Set functions and measures on spaces with additional structure
28D05 Measure-preserving transformations
- PM: measure-preserving, id=1950 -- WP: measure-preserving -- Status: A
28D20 Entropy and other invariants
- PM: entropy of a partition, id=6076 -- WP guess: entropy of a partition -- Status:
- PM: metric entropy, id=6077 -- WP guess: metric entropy -- Status:
28Dxx Measure-theoretic ergodic theory
28E99 Miscellaneous
- PM: proof of pseudoparadox in measure theory, id=6233 -- WP guess: proof of pseudoparadox in measure theory -- Status:
- PM: proof that a finite collection of sets will not suffice, id=6234 -- WP guess: proof that a finite collection of sets will not suffice -- Status:
- PM: pseudoparadox in measure theory, id=6232 -- WP guess: pseudoparadox in measure theory -- Status: