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YCor
YCor
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Open sets with infinite Is every closed subset of finite measure contained in an open subset of finite measure?

Could someone will verify my statement: For every locally finite Borel mesauremeasure on metric space and closed set $F$ with finite measure, there exists open set $U$ such that $F \subset U$ and $U$ has finite measure ?

Open sets with infinite measure

Could someone will verify my statement: For every locally finite Borel mesaure on metric space and closed set $F$ with finite measure, there exists open set $U$ such that $F \subset U$ and $U$ has finite measure ?

Is every closed subset of finite measure contained in an open subset of finite measure?

Could someone will verify my statement: For every locally finite Borel measure on metric space and closed set $F$ with finite measure, there exists open set $U$ such that $F \subset U$ and $U$ has finite measure ?

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Michael
Michael
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Open sets with infinite measure

Could someone will verify my statement: For every locally finite Borel mesaure on metric space and closed set $F$ with finite measure, there exists open set $U$ such that $F \subset U$ and $U$ has finite measure ?