Measure, Integration & Real Analysis · Problem 2D.8

Integration — Sheldon Axler

Mathematics — Measure Theory · lebesgue-measurable-translation-invariant

Problem

Prove that the collection of Lebesgue measurable subsets of

\mathbf{R}

is translation invariant. More precisely, prove that if

A \subseteq \mathbf{R}

is Lebesgue measurable and

t \in \mathbf{R}

, then

t + A

is Lebesgue measurable.