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arXiv · 1410.1967

A fixed point theorem and the existence of a Haar measure for hypergroups satisfying conditions related to amenability

Benjamin Willson
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Abstract

In this paper we present a fixed point property for amenable hypergroups which is analogous to Rickert's fixed point theorem for semigroups. It equates the existence of a left invariant mean on the space of weakly right uniformly continuous functions to the existence of a fixed point for any action of the hypergroup. Using this fixed point property, a certain class of hypergroups are shown to have a left Haar measure.

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Benjamin Willson. 2014-10-08. A fixed point theorem and the existence of a Haar measure for hypergroups satisfying conditions related to amenability. https://doi.org/10.4153/cmb-2014-069-3

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