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is somewhat unsatisfactory: we use the notion of closure, but we do not even have a topology on What we really want to know is where in the space the measure is non-zero. Consider two examples:
# Lebesgue measure on the real line It seems clear that "lives on" the whole of the real line.
# A Dirac measure at some point Again, intuition suggests that the measure "lives at" the point and nowhere else.

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