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Continuity set

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In measure theory, a branch of mathematics, a continuity set of a measure μ is any Borel set B such that

where is the (topological) boundary of B. For signed measures, one asks that

The class of all continuity sets for given measure μ forms a ring.[1]

Similarly, for a random variable X, a set B is called continuity set if

Continuity set of a function

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The continuity set C(f) of a function f is the set of points where f is continuous.

References

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  1. ^ Cuppens, R. (1975) Decomposition of multivariate probability. Academic Press, New York.