Hi,

I have a question concerning integration theory I can't figure out, maybe someone can help:

Fix $\varepsilon>0$ and consider $\delta \colon [0,1] \to (0,\infty)$ measurable. Is it then true that $$\inf_{N\subset [0,1], \lambda(N)>\varepsilon} \int_N \delta(t) dt > 0$$ where $\lambda(N)$ is the Lebesgue measure of $N$?

Thank you!