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- W1992261836 abstract "The structure of idempotent probability measures on compact topological semigroups is well known (see, for example, [2], [41, [7] and [9]). However, the statement in [8] that the methods of [7] can be used to obtain identical results when the semigroup is only semitopological (i.e. the multiplication is separately rather than jointly continuous) is misleading, since the minimal ideal of a compact semitopological semigroup may not be closed [1, Chapter IV, Example 7.1]. In this note, it will be indicated how the convolution decomposition of a probability idempotent may be achieved in the semitopological case. Let S be a compact semitopological semigroup. For each continuous function f on S and each pair x, y of elements of S, we write xf(y) =f(xy) and f.(y) =f (yx). If v is a Radon measure on S we put K(f) = ff (x)dv(x), and define f (x) = v(fT) and f,(x) =v(Jf); the functions Jf and fv are continuous (see [3]). If X is any other Radon measure on S, the mapping (x, y)-*f(xy) is measurable with respect to the product measure X?v (see [5] or [6]), and (using the Fubini Theorem) we may define the convolution product X * v by writing" @default.
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- W1992261836 date "1969-02-01" @default.
- W1992261836 modified "2023-09-25" @default.
- W1992261836 title "Idempotent probability measures on compact semitopological semigroups." @default.
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- W1992261836 doi "https://doi.org/10.1090/s0002-9939-1969-0237750-9" @default.
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