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Does Measure of the support of a Borel probability measure always have full measure inon a metric space?

Does the support of a Borel probability measure always have full measure in a metric space?

I know this is true for separable metric spaces, and locally compact metric spaces, but is. Is it true in general?

Does the support of a Borel probability measure always have full measure in a metric space?

I know this is true for separable metric spaces, and locally compact metric spaces, but is it true in general?

Measure of the support of a Borel probability on a metric space

Does the support of a Borel probability measure always have full measure in a metric space?

I know this is true for separable metric spaces, and locally compact metric spaces. Is it true in general?

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Does the support of a Borel probability measure always have full measure in a metric space?

I know this is true for separable metric spaces, and locally compact metric spaces, but is it true in general?