I want to ask if it is true in general topological space that the countable union of sets of measure $0$ has $0$ measure?
Countable union of measure $0$ sets has measure $0$
2
$\begingroup$
measure-theory
-
4It is true in general *measure spaces* as a consequence of countable additivity. – 2012-04-15
-
2On the other hand, a countable union of *meager sets* is meager, in any topological space (meager means it is a countable union of nowhere dense subsets). Meager sets are the usual notion of "negligible" in the context of topological spaces, while "contained in a set of measure zero" is the usual notion of "negligible" in measure spaces. – 2012-04-15