# Math Help - Integrable Function

1. ## Integrable Function

Let (X,M, $\mu$) be a measure space and let $f\in L^{+}$ be integrable ( $\int$ $f$ $d\mu$< $\infty$). Show that for each $\epsilon$ > 0 there is a $\delta$ > 0 such that if A $\subset$ X and $\mu(A)$< $\delta$,
then $\int$ $f$< $\epsilon$ where the integral is calculate over the subset A. Show that the result may fail if the assumption on the integrability of f is dropped.

2. ## Re: Integrable Function

First, consider the case for which f is a simple function.