If f is a strictly positive Riemann integrable function defined on a closed and bounded interval. Then, is it necessary that f has strictly positive Riemann integral value?
f need not be continuous.
I was trying to construct some example similar to Thomae function but such that it is strictly positive but in that case I was getting integral to be strictly positive.
[Math] Is the Riemann integral of a strictly positive function strictly positive
calculusintegrationreal-analysis
Best Answer
Hint: The set of discontinuity points of a Riemann integrable function has Lebesgue measure zero. In particular, it is continuous at some point of the interval.