The volume of null-set

355 Views Asked by At

I saw this claim:

if $v(E)$ = 0, then E is a null-set. The converse statement is wrong.

where $v(E)$ is the Jordan measure of $E$,

I am not sure if this right, because I know $\int_E1_E=0 $ for $E$ null set and for any bounded function.