Measure, Integration & Real Analysis · Problem 4A.8

Product Measures — Sheldon Axler

Mathematics — Measure Theory · hardy-littlewood-maximal-function-ramp

Problem

Find a formula for the Hardy–Littlewood maximal function of the function

h: \mathbf{R} \to [0, \infty)

defined by

h(x) = \begin{cases} x & \text{if } 0 \leq x \leq 1, \\ 0 & \text{otherwise.} \end{cases}