I read the following convolution property in a proof of conservation of energy by Vlasov-Poisson. I tried to prove it without success.
$$\int (f * g)(x) \,h(x)\, dx = \int f(x)\,(g*h)(x) \,dx$$
With $(f*g)(x)=\int f(y)\,g(x-y)\,dy$
Is there someone who can help me to show this or give me a counter-example?