On repeated sequential closures of constructible functions in valuations
Metric Geometry
2015-06-16 v3 Functional Analysis
Abstract
The space of constructible functions form a dense subspace of the space of generalized valuations. In this note we prove a somewhat stronger property that the sequential closure, taken sufficiently many (in fact, infinitely many) times, of the former space is equal to the latter one. This stronger property is necessary for some applications in the theory of valuations on manifolds.
Cite
@article{arxiv.1408.2637,
title = {On repeated sequential closures of constructible functions in valuations},
author = {Semyon Alesker},
journal= {arXiv preprint arXiv:1408.2637},
year = {2015}
}
Comments
13 pages; Lemma 2.6 added; minor corrections