Let $(varOmega, varSigma ,mu)$ be a finite measure space and $X$ be a separable Banach space. For $1 leq p leq infty$, let $L_{p}(mu,X)$ denote the class of all $mu$-Bochner integrable functions $f$ such that $|f|_{p} = (int_{varOmega} |f|^{p})^{1/p} < infty$.

If $Phi in L_{p}(mu,X)$ and $h: X rightarrow X$ is a continuous function, then is $h circ Phi in L_{p}(mu,X)$?