Measure, Integration & Real Analysis · Problem 2B.6

Measures — Sheldon Axler

Mathematics — Measure Theory · measurable-function-condition-rationals

Problem

Suppose (X,S)(X, \mathcal{S}) is a measurable space and f:X→Rf : X \to \mathbf{R} is a function such that f−1((r,∞))∈Sf^{-1}((r, \infty)) \in \mathcal{S} for all r∈Qr \in \mathbf{Q}. Show that ff is an S\mathcal{S}-measurable function.

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