Measure, Integration & Real Analysis · Problem 2B.17

Measures — Sheldon Axler

Mathematics — Measure Theory · measurable-function-condition-52-proof

Problem

Prove result 2.52: Suppose (X,S)(X, \mathcal{S}) is a measurable space and f:X→[−∞,∞]f : X \to [-\infty, \infty] is a function such that f−1((a,∞])∈Sf^{-1}\bigl((a, \infty]\bigr) \in \mathcal{S} for all a∈Ra \in \mathbf{R}. Then ff is an S\mathcal{S}-measurable function.

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