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The uniquenesss of a left Haar measure in topological IP-loops

Abstract In the paper [STEHLÍKOVÁ, B.—MARKECHOVÁ, D.—TIRPÁKOVÁ, A.: On the existence of a Haar measure in topological IP-loops, Kybernetika (Prague) 47 (2011), 740–754] we have proved that in every locally compact topological IP-loop with topology induced by a left-invariant uniformity there exists at least one regular left Haar measure. In this paper, we prove that the regular left Haar measure in a locally compact topological IP-loop is essentially unique.