Measure, Integration & Real Analysis · Problem 11C.12

Probability Measures — Sheldon Axler

Mathematics — Measure Theory · poisson-kernel-semigroup

Problem

Suppose

p \in [1, \infty]

and

f \in L^p(\mathbf{R})

. Prove that

\mathcal{P}_y(\mathcal{P}_{y'} f) = \mathcal{P}_{y+y'} f

for all

y, y' > 0