Let be $u$ a numerical function defined over $\Omega$, with $u$ measurable, and let be $(O_i)_{i\in I}$ a family of all open sub-sets $O_i$ of $\Omega$, such that $u=0$ often in $O_i$. Let be $O = \cup_{i\in I}O_i$. Then $u=0$ often in $O$.
How I can be able to do this?.
I am beginning make ...
Let be $u$ defined than $0$ in $O_i\setminus M_i$ and $\neq$ $0$ in $M_i$, then
$O = \cup_{i\in I}O_i=\cup_{i\in I}[(O_i\setminus M_i)\cup M_i]$, ...
but I don't know how find the subset of $O$ such that have measure zero.