Measure, Integration & Real Analysis · Problem 2C.12

Measures — Sheldon Axler

Mathematics — Measure Theory · measures

Problem

Suppose

X

is a set and

\mathcal{S}

is the

\sigma

-algebra of all subsets

E

X

such that

E

is countable or

X \setminus E

is countable. Give a complete description of the set of all measures on

(X, \mathcal{S})