๐-finite invariant measures on infinite product spaces
๐-finite invariant measures on infinite product spaces
A necessary and sufficient condition in terms of Hellinger integrals is established for the existence of a <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma"> <mml:semantics> <mml:mi>ฯ<!-- ฯ --></mml:mi> <mml:annotation encoding="application/x-tex">\sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-finite invariant measure on an infinite product space. Using this it is possible to construct a wide class of transformations โฆ