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This is an old revision of this page, as edited by 24.1.53.152 (talk) at 05:53, 25 January 2011 (→‎Further example). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

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images and examples

I have created two images, Image:Borelparardox support xydist.png and Image:Borelparardox support uvdist.png, showing the regions on which the two distributions are non-zero. I'm not handy enough at image manipulation and html to insert them into the document, but they're available to anyone who wishes to do so and has the know-how. -- Cyan 21:55, 26 Jan 2004 (UTC)

Credit where credit is due: the example of the paradox that I wrote up was taken, mutatis mutandis, from [1]. -- Cyan 04:06, 27 Jan 2004 (UTC)

Considering the size of the diagrams, I've just linked to them rather than displaying them inline, but I'm not really sure whether that is the best option. Do you think it would be more helpful to display on the page, and if so, do you want them in the positions the links currently are? Angela. 17:14, Jan 27, 2004 (UTC)

I originally imagined them shrunken and inline, but I wasn't sure how to go about it. It didn't occur to me that they could be linked within the article. I am satisfied with the present arrangement; I will rely on the wiki process for improvements. Thanks, Angela! -- Cyan 17:38, 27 Jan 2004 (UTC)

The links to the images don't work. The village pump says: "Note that images uploaded from Jan 24-Jan 28 are unavailable for now; try re-uploading anything you lost." Fpahl 12:33, 5 Apr 2004 (UTC)

another explanation

I'm thinking of adding something about the problem being the artificial precision of an exact condition. The "paradox" does not appear if you specify a small but finite interval as a condition; it relies on the fact that the point-like condition has different relative "precision" in the two coordinate systems. But I'm not sure how much consensus there is on this view of the paradox -- any comments? Fpahl 18:25, 19 Apr 2004 (UTC)

It's the explanation I endorse, although others exist. Go for it. -- Cyan

too technical tag

i removed the tag. if you wish to reinsert it, please do so but leave some suggestions here as to what could be improved or what you find difficult to understand. thanks. Lunch 04:34, 24 September 2006 (UTC)[reply]


example

I think the sphere coordinates example mentioned in this sci.math thread is more illustrative than the current example.--Novwik (talk) 19:15, 17 November 2007 (UTC)[reply]

I agree. I've started to rewrite the article around the spherical example. I also think the article should be Borel-Kolmogorov paradox, as that seems to be the most common reference. -3mta3 (talk) 10:31, 10 March 2009 (UTC)[reply]
Okay, I've rewritten most of it, and tried to emphasise the important concepts as I saw it. I might try and draw some pictures to aid the explanation if I get around to it -3mta3 (talk) 12:19, 11 March 2009 (UTC)[reply]

reconsider canonical example wording

The article says:

"Consider a random point distributed uniformly over the surface of an assumed spherical "earth""

however, this doesn't seem to make sense. How do you distribute 1 point, let alone 1 anything? It's like saying "imagine 1 orange distributed uniformly around your house." —Preceding unsigned comment added by 113.190.136.203 (talk) 15:49, 8 August 2010 (UTC)[reply]

Further example

I like to modify this section with the following text. But I have no reference to published material:

As the great circle puzzle shows, the condition in conditional probability cannot, in general, be an event that has zero measure. In terms of coordinate transformation, let Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle \{x,y,f_{x|y}(x|y)\} \rightarrow \{u=g(x), v=h(y), f_{u|v}(u|v)\}} define a map. Consider the set of points such that . The conditional density functions and are not necessarily invariant at these points by the principle of zero measure conditionality.

To me, this seems rather obvious, but admittedly this is only a conjecture on my part and I do not have a formal proof. If someone knows of a reference, please include this in the body of the article.24.1.53.152 (talk) 23:19, 22 January 2011 (UTC)[reply]