Continuity set
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
![{\displaystyle \Pr[X\in \partial B]=0.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/66b652d80b3f30a1348524bffc085f63dc468aec)
Continuity set of a function
The continuity set C(f) of a function f is the set of points where f is continuous.[citation needed]
References
- ^ Cuppens, R. (1975) Decomposition of multivariate probability. Academic Press, New York.
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