Supposing $f,g, h$ are defined on $\Bbb R$ and are all integrable on $\Bbb R$. Define their convolution as $f * g (z) = \int_{\Bbb R} f(x) g (z-x) dx$. Now I wish to show that this operation is associative, i.e. that $(f*(g*h))(x)=((f*g)*h)(x)$.
I'm not even sure what the left side of the equation should be. Is it that :
$(f*(g*h))(z)=\int_{\Bbb R}f(x) \cdot (\int_{\Bbb R} g(z-y)h(z-(z-y)) dy)dx$ ?
Hints and insights appreciated.