Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How could I show "integral of a nonnegative measurable function f could be defined as the infimum of a set of integrals of simple functions g with f<=g for all g".

We could assume f is bounded by M. Then M-f is nonnegative measurable. How to proceed further from here?

Help is appreciated!

share|improve this question

1 Answer 1

Take a look at $f(x) = e^{-x}$ on $[0,\infty)$. Do you see the problem?

share|improve this answer
    
If the function is bounded above on a bounded interval, your formulation would work. –  ncmathsadist Apr 7 '13 at 2:43
    
If I assume f is bounded above on any measurable set A with the measure of A being finite, would my formulation be correct? If so, any hint on how to prove it? –  user65214 Apr 7 '13 at 2:58

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.