Let $ f \in L^1_{loc}(\mathbb R^n)$ and $ \varphi $ a mollifier, consider $\varphi_{\varepsilon}:=\frac{1}{\varepsilon ^n} \varphi \left( \frac{x}{\varepsilon} \right)$ show that $f * \varphi_{\varepsilon}(E)$ is contained in the closed convex hull of $f(E)$, $\forall E \subset \mathbb R^n$
I try to use some properties of the convolution like continuity, but i not sure if these is correct, i not have idea can procedure in these problem.
Any hint or help i will be very grateful