Measure, Integration & Real Analysis · Problem 2B.19

Measures — Sheldon Axler

Mathematics — Measure Theory · measurable-functions

Problem

Suppose

X

is a nonempty set and

\mathcal{S}

is the

\sigma

-algebra on

X

consisting of all subsets of

X

that are either countable or have a countable complement in

X

. Give a characterization of the

\mathcal{S}

-measurable real-valued functions on

X