Exercise 25, § 4

Let G be a locally compact group, β a left Haar measure on G, μ a positive measure on G. If A is a μ-integrable set and B is a Borel set in G, the function

is β-measurable in G; if, in addition, B^{-1} is β-integrable, then so is u, and

Give an example of a measure $\mu$ such that $s \mapsto \mu(A \cap sB)$ is not continuous; if $\mu$ is a measure with base $\beta$, and if $A$ is $\mu$-integrable and $B$ is a Borel set, then the function $s \mapsto \mu(A \cap sB)$ is continuous on $G$.