My analysis professor, a few weeks ago, when we were talking about integrability, introduced the concept of Lebesgue measure zero. He put up a theorem stating that the set of discontinuities of a function are of Lebesgue measure zero if and only if the function is integrable. This is, of course, after defining lebesgue measure zero. I've tried to google for this and haven't found it. Is it normally introduced in an introductory real analysis class? Where exactly does Lebesgue measure come about from? References to books, etc. would be appreciated.