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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.

  • 2
    Does "often" mean "almost always", that is "except on a set of measure $0$"?2012-09-27
  • 0
    Are we in Euclidean space here? And is $I$ supposed to be countable?2012-09-27
  • 0
    @AlexBecker yes2012-09-27
  • 0
    @HaraldHanche-Olsen yes2012-09-27

1 Answers 1