Measure theory MOC

Locally finite measure

Let 𝑋 be a Hausdorff topological space (𝑋,T) and a measure space (𝑋,Σ,𝜇) at with Σ least as fine as a Borel algebra, i.e. T ⊆Σ. Then 𝜇 is locally finite iff every 𝑥 ∈𝑋 has a neighbourhood 𝑈 such that 𝜇(𝑈) is finite. #m/def/measure

Properties

• Local finite measure of a compact set is finite

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