Measure, Integration & Real Analysis · Problem 4B.6

Product Measures — Sheldon Axler

Mathematics — Measure Theory · lebesgue-differentiation-integral-zero

Problem

Prove that if

h \in \mathcal{L}^1(\mathbf{R})

and

\int_{-\infty}^s h = 0

for all

s \in \mathbf{R}

, then

h(s) = 0

for almost every

s \in \mathbf{R}