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The primary objective in these notes is to provide the reader with brief, but somewhat complete account of the theory of probability and measure on topological semigroups in the context of the following problems: (i) the characterizations of the idempotent and r*-invariant probability measures on locally compact Hausdorff topological semigroups (ii) the limit behavior of the averaged and unaveraged sequence of convolution iterates of probability measures on different topological semigroups, and also on semigroups of stochastic matrices (iii) almost sure convergence of products of independent random variables taking values in a completely simple semigroup and (iv) the recurrence behavior of one-sided and two-sided random walks induced by a probability measure on a compact Hausdorff or locally compact Hausdorff completely simple topological semigroup.
The primary objective in these notes is to provide the reader with brief, but somewhat complete account of the theory of probability and measure on topological semigroups in the context of the following problems: (i) the characterizations of the idempotent and r*-invariant probability measures on...
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