A separable metric space is strongly Lindelof, that is, every open cover of an open subset has a countable subcover. The complement of the support is the union of all open balls with zero measure. By reducing to a countable subcover, we see that this set has measure zero. So the support has full measure.
|
2 | deleted 9 characters in body | ||
|
|
||||
|
|
1 |
|
||
|
A separable metric space is strongly Lindelof, that is, every open cover of an open subset has a countable subcover. The complement of the support is the union of all open balls with zero measure. By reducing to a countable subcover, we see that this set has measure zero. So the support has full measure. |
||||
