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SummaryThe structure of the support F of an idempotent probability measure Μ on a locally compact semigroup S is considered. It is shown that if S satisfies the condition (L): AB−1 is compact… (More)

A conjecture stating that a locally compact semigroup admits a twosided semi-invariant measure iff it contains a kernel which is a unimodular group, is proven. Also a conjecture stating that the… (More)

For B c S , B x -1 =t~l(B) { s e S ; s x e B } and in particular for x, y e S , x y l =_ {s ~ S ; s y -~ x}. tx denotes the (continuous) right translation s --> sx . # is called r*-invariant if tt (… (More)

Let S be a Hausdorff topological semigroup and C b ,( S ), C c ( S ), the spaces of real valued continuous functions on S which are respectively bounded and have compact support. A regular measure m… (More)

Let /i be a regular Borel probability measure with support F on a compact semigroup S. Let XO, X+1, X+2-.. be a sequence of independent random variables with values in S, having identical… (More)

where tx denotes the (continuous) right translation s ~ s x . Let Cb(S) and Co(S) be the space of all real valued continuous functions on S which are bounded and have compact supports respectively.… (More)