The assertion every Radon measure defined on a first-countable compact space is uniformly regular is shown to be relatively consistent. We prove an analogous result on the existence of uniformly distributed sequences in compact spaces of small character. We also present two related examples constructed under CH.
@article{bwmeta1.element.bwnjournal-article-cmv86i1p15bwm,
author = {Grzegorz Plebanek},
title = {Approximating Radon measures on first-countable compact spaces},
journal = {Colloquium Mathematicae},
volume = {84/85},
year = {2000},
pages = {15-23},
zbl = {0996.28005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv86i1p15bwm}
}
Plebanek, Grzegorz. Approximating Radon measures on first-countable compact spaces. Colloquium Mathematicae, Tome 84/85 (2000) pp. 15-23. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv86i1p15bwm/
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