## Examples 7.4.17(d): Lebesgue Integral of Non-Negative Function

Suppose

*f*is a non-negative integrable function such that*. Show that then*_{E}f(x) dx = 0*f = 0*except on a set of measure zero.
Suppose *f* is a non-negative integrable function such that
_{E} f(x) dx = 0.
Show that then *f = 0* except on a set of measure zero.