Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 1 ,pp. 49-56

A REMARK ON MEASURE PRESERVING TRANSFORMATIONS ON POLISH SPACES AND APPLICATION TO MARTINGALE PRESERVING TRANSFORMATIONS

By

DEBASHISH GOSWAMI, Indian Statistical Institute, New Delhi

SUMMARY.We give a characterization of isometries induced by measure preserving maps on Polish spaces equipped with a probability measure and generalize a result of Attal (1995) on martingale preserving endomorphisms of Wiener space as an application, entirely by classical techniques.

AMS (1991) subject classification. 28D05.

Key words and phrases. Measure preserving transformations, isometry, Polish spaces.

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