So I have a measurable, non-negative functionf. I am to show that the integral offwith respect toxis zero if and only if the set ofxsthat makef(x)> 0 is a set of measure zero. To show the first half of this implication, I am using a contrapositive argument. My classmate suggested that I use simple functions to approximate the integral below, but I'm not sure how to do this. Any thoughts?

rogerpodger