1. Apr 8, 2010

### AxiomOfChoice

Suppose you have a nonnegative Lebesgue measurable function supported on $$[0,1]$$ such that $$\int_0^1 f = \infty$$. Does this mean that the set $$E = \{ x\in [0,1] : f(x) = \infty \}$$ has positive Lebesgue measure?

2. Apr 8, 2010

### JSuarez

No. Consider the function $f\left(x\right)=1/x$, and whatever value you want at x = 0.