$m ( \{ x : f(x) > 0 \} ) = 0 \implies f = 0 $ almost everywhere

$m ( \{ x : f(x) > 0 \} ) = 0 \implies f = 0 $ almost everywhere

Suppose $f$ is non-negative measurable function. Put $E = \{ x : f(x) > 0
\} $.
Say $m(E) = 0$. In other words, $E$ is null set. Then does it follow that
$f = 0 $ almost everywhere ?