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

Measures — Sheldon Axler

Mathematics — Measure Theory · outer-measure-scaling

Problem

Suppose

A \subseteq \mathbf{R}

and

t \in \mathbf{R}

. Let

tA = \{ta : a \in A\}

. Prove that

|tA| = |t|\,|A|

. [Assume that

0 \cdot \infty

is defined to be

0