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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 instead asks that

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

Similarly, for a random variable X, a set B is called a continuity set of X 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.[citation needed]

References

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