Walter Bloom

A systematic presentation of the applications of the hypergroup method to problems in probability theory that deals exclusively with topological hypergroups, focusing on those that are commutative. It considers hypergroups as locally compact spaces with a group-like structure on which the bounded measures convolve in a similar way to that on a locally compact group. The volume covers hypergroups and their measure algebras, the dual of a commutative hypergroup, some special classes of hypergroups, positive and negative definite functions and measures, convolution semigroups and divisibility of measures, transience of convolution semigroups, and randomized sums of hypergroup-valued random variables...