Measure, Integration & Real Analysis · Problem 2B.2

Measures — Sheldon Axler

Mathematics — Measure Theory · sigma-algebra-smallest-example

Problem

Verify that the smallest σ\sigma-algebra on XX containing A={{x}:x∈X}\mathcal{A} = \{\{x\} : x \in X\} is the set of all subsets EE of XX such that EE is countable or X∖EX \setminus E is countable.

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