Continuity set

From HandWiki

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

μ(B)=0,

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

|μ|(B)=0.

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

Pr[XB]=0.

Continuity set of a function

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

References

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