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A set of positive Gaussian measure with uniformly zero density everywhere
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Preiss, David, Riss, Elena and Tišer, Jaroslav (2021) A set of positive Gaussian measure with uniformly zero density everywhere. Journal of the European Mathematical Society, 23 (7). pp. 2439-2466. doi:10.4171/JEMS/1058 ISSN 1435-9855.
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Official URL: https://doi.org/10.4171/JEMS/1058
Abstract
Existing negative results on invalidity of analogues of classical Density and Differentiation Theorems in infinite dimensional spaces are considerably strengthened by a construction of a Gaussian measure γ on a separable Hilbert space H for which the Density Theorem fails uniformly, i.e., there is a set M⊂H of positive γ-measure such that
Lim sup γ(B(x, r)∩M)
__________ = 0:
r\0 x∈H γB(x, r)
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Gaussian measures, Hilbert space | ||||||||||||
| Journal or Publication Title: | Journal of the European Mathematical Society | ||||||||||||
| Publisher: | European Mathematical Society Publishing House | ||||||||||||
| ISSN: | 1435-9855 | ||||||||||||
| Official Date: | 25 March 2021 | ||||||||||||
| Dates: |
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| Volume: | 23 | ||||||||||||
| Number: | 7 | ||||||||||||
| Page Range: | pp. 2439-2466 | ||||||||||||
| DOI: | 10.4171/JEMS/1058 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
| Copyright Holders: | European Mathematical Society 2019 | ||||||||||||
| Date of first compliant deposit: | 21 May 2019 | ||||||||||||
| Date of first compliant Open Access: | 22 May 2019 | ||||||||||||
| RIOXX Funder/Project Grant: |
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