A characterisation of absolutely continuous measures on topological semigroups
A characterisation of absolutely continuous measures on topological semigroups
Let <italic>S</italic> be a completely regular topological semigroup and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="mu"> <mml:semantics> <mml:mi>μ<!-- μ --></mml:mi> <mml:annotation encoding="application/x-tex">\mu</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a bounded regular Borel measure on <italic>S</italic>. For a very large class of noncompact semigroups <italic>S</italic>, we show that the map <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x right-arrow …