![]() |
![]() |
University of Birmingham > Talks@bham > Analysis Seminar > The Steinhaus-Weil property: its converse, Solecki amenability and subcontinuity
The Steinhaus-Weil property: its converse, Solecki amenability and subcontinuityAdd to your list(s) Download to your calendar using vCal
If you have a question about this talk, please contact Andrew Morris. The Steinhaus-Weil theorem that concerns us is the `interior points’ property—that in a topological group a non-negligible set S has the identity as an interior point of S⁻¹S. 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 reference measure η. 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. We exploit the connection between the interior points property and a selective form of infinitesimal invariance afforded by a certain family of selective reference measures σ, drawing on Solecki’s amenability at 1 (and using Fuller’s notion of subcontinuity. We may thereby develop a number of relatives of the Simmons-Mospan theorem. This has links with topologies of Weil type. This talk is part of the Analysis Seminar series. This talk is included in these lists:Note that ex-directory lists are not shown. |
Other listsSpeech Recognition by Synthesis Seminars Birmingham Popular Maths Lectures School of Metallurgy and Materials ColloquiaOther talksPrediction of Toric Code Topological Order from Rydberg Blockade Outerspacial 2-complexes Roots of random functions Variational Bayesian inference for point processes - a latent variable approach Principal Component Analysis of Quantum Materials Data: a Study in Augmented Intelligence |