I tried to solve the problem in Stein's Real analysis, 1ed, P94, Ex 21 (c), which asked to show that for any two measurable functions $f,g$ on $R^d$, the convolution of $f$ and $g$, $$(f\ast g)(x)=\int_{R^d}f(x-y)g(y)dy$$ is well defined for a.e. $x$, i.e., $f(x-y)g(y)$ is integrable on $R^d$ for a.e. $x$.
If $f,g$ are integrable, this will be easy conclusion of $(a)$ and $(b)$, but it seems form $(d)$, that the integrability of $f,g$ are not assumed here!
From wiki: https://en.wikipedia.org/wiki/Convolution#Domain_of_definition we know that $f\ast g$ is only defined for some classes of $f$ and $g$, if $f,g$ are only measurable, I do suspect that the convolution is well defined.