Beyond Haar and Cameron-Martin: the Steinhaus support

Bingham, N. H.; and Ostaszewski, AdamORCID logo (2019) Beyond Haar and Cameron-Martin: the Steinhaus support Topology and its Applications, 260. 23 - 56. ISSN 0166-8641
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Motivated by a Steinhaus-like interior-point property involving the Cameron-Martin space of Gaussian measure theory, we study a grouptheoretic analogue, the Steinhaus triple (H, G, μ), and construct a Steinhaus support, a Cameron-Martin-like subset, H(μ) in any Polish group G corresponding to ‘sufficiently subcontinuous’ measures μ, in particular for ‘Solecki-type’ reference measures.
Item Type Article
Copyright holders © 2019 Elsevier B.V.
Keywords Abstract Wiener space, Amenability at 1, Cameron-Martin space, Gaussian measures, Measure subcontinuity, Relative quasi-invariance, Relativized Steinhaus (interior-point) property, Steinhaus support, Steinhaus triple
Departments Mathematics
DOI 10.1016/j.topol.2019.03.020
Date Deposited 28 Mar 2019 10:39
Acceptance Date 2019-03-16
URI https://researchonline.lse.ac.uk/id/eprint/100369

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