I am just learning about convolutions in a measure theory course. We are given that the convolution of two functions $f$ and $g$ is defined as:
$$f*g(t) = \int f(u)g(t-u) \,du$$
Now, I would like to show that, if $f$ and $g$ are continuous with compact support, then the convolution $f*g$ is also continuous. I can't seem to wrap my head around how to show this.