A THEOREM ON COMPACT SIMPLE SEMIGROUPS
COLUMBIA UNIV NEW YORK
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Proof is given for th e conjecture of M. Rosenblatt J. Math. and Mech. 9293-306, 1960 concerning the factorization of idempotent probability measures on compact simple semigroups. The measures are shown to contain factors of Haar measure on a compact topological group and probability measures on two compact Hausdorff spaces.