Continuity set

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

\mu (\partial B)=0\,,

where $\partial B$ is the boundary set of B. For signed measures, one asks that

|\mu |(\partial 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[X\in \partial B]=0

Continuity set of a function

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

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gollark: That's a nice infographic. I like the hexagons.

gollark: (my internet connection is very unstable right now, I'm having to type very slowly on my phone)

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

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