Sequential closure in the space of measures

Details Sequential closure in the space of measures Sequential closure in the space of measures

2012-03-19

arxiv.org/abs/1203.4270v1

Mathematics

General Topology

Scientific paper

We show that there is a compact topological space carrying a measure which is not a weak* limit of finitely supported measures but is in the sequential closure of the set of such measures. We construct compact spaces with measures of arbitrarily high levels of complexity in this sequential hierarchy. It follows that there is a compact space in which the sequential closure cannot be obtained in countably many steps. However, we show that this is not the case for our spaces where the sequential closure is always obtained in countably many steps.

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