continuity set
In measure theory, a branch of mathematics, a continuity set of a measure {{mvar|μ}} is any Borel set {{mvar|B}} such that
where is the (topological) boundary of {{mvar|B}}. For signed measures, one instead asks that
The collection of all continuity sets for a given measure {{mvar|μ}} forms a ring of sets.Cuppens, R. (1975) Decomposition of multivariate probability. Academic Press, New York.
Similarly, for a random variable {{mvar|X}}, a set {{mvar|B}} is called a continuity set of {{mvar|X}} if
Continuity set of a function
The continuity set {{math|C(f)}} of a function {{mvar|f}} is the set of points where {{mvar|f}} is continuous.{{citation needed|date=February 2025}}