On Quasi-invariance of Infinite Product Measures

Gaku Sadasue ()
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Gaku Sadasue: Osaka Kyoiku University

Journal of Theoretical Probability, 2008, vol. 21, issue 3, 571-585

Abstract: Abstract Quasi-invariance of infinite product measures is studied when a locally compact second countable group acts on a standard Borel space. A characterization of l 2-quasi-invariant infinite product measures is given. The group that leaves the measure class invariant is also studied. In the case where the group acts on itself by translations, our result extends previous ones obtained by Shepp (Ann. Math. Stat. 36:1107–1112, 1965) and by Hora (Math. Z. 206:169–192, 1991; J. Theor. Probab. 5:71–100, 1992) to all connected Lie groups.

Keywords: Infinite product measure; Quasi-invariance; Quasi-invariant subgroup; G-space; 22D40 (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10959-008-0171-9

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