Union of Sets in Locally Compact Hausdorff Space
Is it possible for an open set in a locally compact Hausdorff space to not
be the union of an increasing sequence of compact sets? If so, given a
regular Borel measure on such a space, how is it that the limit of the
measures of the compact sets is equal to measure of the open set? How far
can this disconnect be pushed; that is, what conclusion can be made about
the union of the increasing sequence of compact sets relative to the open
set, other than the limit of the measures is the measure of the limit?
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