Let f be a positive, measurable function. Let c be a constant. let E be a measurable set.

I know that the integral of cf over E equals c times the integral of f over E when c is greater than or equal to 0 and less than infinity. I need to prove that this works even when c= infinity. I am a little confused because isn't infinity times a positive value infinity? I suppose 0 times infinity is 0. Does it suffice to just look at these two cases?