Measure, Integration & Real Analysis · Problem 2C.5

Measures — Sheldon Axler

Mathematics — Measure Theory · measures

Problem

Suppose (X,S,μ)(X, \mathcal{S}, \mu) is a measure space such that μ(X)<∞\mu(X) < \infty. Prove that if A\mathcal{A} is a set of disjoint sets in S\mathcal{S} such that μ(A)>0\mu(A) > 0 for every A∈AA \in \mathcal{A}, then A\mathcal{A} is a countable set.

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