Lebesgue integration/Talk

Look - I'm sure that this is a well-writen article, but could someone (knowledgeable) put in a 2-3 line explanation of what it actually about, and what it is used for? The opening sentence "Let m be ..." isn't really au fait in a generalist encyclopedia. I'm really glad we have this sort of advanced stuff, but in this case I don't even understand what I don't understand. - MMGB

Shouldn't it be at some point made clear that m is the Lebesgue measure? Otherwise, there's no guarantee the integral will correspond to Riemann integration - if m is the counting measure, it will correspond to summation. But I'm not sure where precisely to work that in.