I can't make up my mind if this statement is true or not: is it true that if we assume g is integrable and g[tex]\geq[/tex]0 on [a,b], then if g(x)[tex]\geq[/tex]0 for an infinite number of points x is in [a,b] then [tex]\int[/tex] g >0. I can't figure out if its true or false, i thought that i had a counter example: if g>0 at a single point i.e. g(a)=1 and g=0 otherwise, then g is integrable and non negative, and the set of discontinuities must be finite. I don't know if this is exactly right. Any help please?