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arXiv · 2012.02866

Conglomerated filters, statistical measures, and representations by ultrafilters

Vladimir Kadets·Dmytro Seliutin
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Abstract

Using a new concept of conglomerated filter we demonstrate in a purely combinatorial way that none of Erd\"{o}s-Ulam filters or summable filters can be generated by a single statistical measure and consequently they cannot be represented as intersections of countable families of ulrafilters. Minimal families of ultrafilters and their intersections are studied and several open questions are discussed.

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BibTeXRIS

Vladimir Kadets, Dmytro Seliutin. 2020-12-04. Conglomerated filters, statistical measures, and representations by ultrafilters. https://arxiv.org/abs/2012.02866

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