The Solecki submeasures on groups

Prelegent(ci)

Taras Banakh

Afiliacja

Lviv National University i UJK Kielce

Termin

21 listopada 2012 16:15

Pokój

p. 5050

Seminarium

Seminarium „Topologia i teoria mnogości”

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The {\em Solecki submeasure} $\sigma$ on a group $G$ is the invariant monotone subadditive function assigning to each subset $A\subset G$ the real number $\sigma(A)=\inf_\sup_{x,y\in G}|F\cap xAy|/|F|$ where the infimum is taken over all non-empty finite subsets $F$ of $G$. In this paper we study the properties of the Solecki submeasure and its left and right modifications on (topological)groups and establish an interplay between the Solecki submeasure and the Haar measure on a compact topological group $G$. In particular, we show that the Haar measure on a compact topological group is uniquely determined by the Solecki submeasure. More details can be found at http://arxiv.org/abs/1211.0717.

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