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Continuity set

In measure theory, a branch of mathematics, a continuity set of a measure μ is any Borel set B such that μ ( ∂ B ) = 0 , {\displaystyle \mu (\partial B)=0,} where ∂ B {\displaystyle \partial B} is the (topological) boundary of B. For signed measures, one instead asks that | μ | ( ∂ B ) = 0. {\displaystyle |\mu |(\partial B)=0.}

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Continuity set of a function

FunctionContinuous
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Measure theoryMathematicsMeasureBorel setBoundary
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Continuity set of a function

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Continuity set

Nodes13
Edges12
Triples1
Avg. degree1.85
Density0.153846
Components1

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Continuity set

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continuity set displaystyle partial measure mu pr function mathematics boundary theory branch borel topological signed measures one instead asks collection

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Continuity setrelated to Continuity set of a functionThe0.60section

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