Structure hypergroups for measure algebras
Charles F. Dunkl · Pacific Journal of Mathematics · 1973
An abstract measure algebra A is a Banach algebra of measures on a locally compact Hausdorff space X such that the set of probability measures in A is mapped into itself under multiplication, and if μ is a finite regular Borel measure on X and μ \ \ fd\(x, y)dv(y) JxJx is continuous andThis fact was proved by Glicksberg [3].We will use this to define semitopological hypergroups.DEFINITION 1.1.A locally compact space H is called a semitopological hypergroup if there is a map λ: H x H-+M P (H) with the following properties:(1) X(x, y) = X(y, x), {x, yeH), (commutativity);(2) for each fe C 0 (H) the map (x, y) i-> I fdX(x.y) is separately JH continuous, (α?, yeH);