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Article overview
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The Steinhaus-Weil property: its converse, Solecki amenability and subcontinuity | N. H. Bingham
; A. J. Ostaszewski
; | Date: |
30 Jun 2016 | Abstract: | The Steinhaus-Weil theorem that concerns us here is the ’interior points’
property -- that in a topological group a non-negligible set S has the identity
as an interior point of $SS^{-1}$. There are various converses; the one that
mainly concerns us is due to Simmons and Mospan. Here the group is locally
compact, so we have a Haar measure. The Simmons-Mospan theorem states that a
(regular Borel) measure has such a Steinhaus-Weil property if and only if it is
absolutely continuous with respect to the Haar measure. In Part I (Propositions
1-9, Theorems 1-3) we develop a number of relatives of the Simmons-Mospan
theorem, drawing also on Solecki’s amenability at 1 (and using Fuller’s notion
of subcontinuity). In Part II (Theorems 4, 5) we link this with topologies of
Weil type. | Source: | arXiv, 1607.0049 | Services: | Forum | Review | PDF | Favorites |
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