# measure theory – Bochner integrability of composition of continuous and Bochner integrable function

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 $$h circ Phi in L_{p}(mu,X)$$?