A generalized converse measurability theorem

Authors:
K. S. Chang and K. S. Ryu

Journal:
Proc. Amer. Math. Soc. **104** (1988), 835-839

MSC:
Primary 28C20

DOI:
https://doi.org/10.1090/S0002-9939-1988-0935104-2

MathSciNet review:
935104

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Abstract | References | Similar Articles | Additional Information

Abstract: It has long been known that measurability questions in Wiener space and Yeh-Wiener space are often rather delicate. Some converse measurability theorems in Wiener and Yeh-Wiener spaces were proved by Köehler, Skoug, and the first author.

In this paper, we establish a generalized converse measurability theorem by which the above measurability theorems are proved as corollaries.

**[1]**R. H. Cameron and D. A. Storvick,*Two related integrals over spaces of continuous functions*, Pacific J. Math.**55**(1974), 19-37. MR**0369649 (51:5881)****[2]**K. S. Chang,*Converse measurability theorems for Yeh-Wiener space*, Pacific J. Math.**97**(1981), 59-63. MR**638171 (83g:60067)****[3]**K. S. Chang and I. Yoo,*A simple proof of converse measurability theorem for Yeh-Wiener spaces*, Bull. Korean Math. Soc.**23**(1986), 35-37. MR**843206 (87m:60178)****[4]**K. R. Parthasarathy,*Probability measures on metric space*, Academic Press, New York, 1967. MR**0226684 (37:2271)****[5]**D. L. Skoug,*Converses to measurability theorems for Yeh-Wiener space*, Proc. Amer. Math. Soc.**57**(1976), 304-310. MR**0422563 (54:10549)****[6]**J. Yeh,*Wiener measure in a space of functions of two variables*, Trans. Amer. Math. Soc.**95**(1960), 433-450. MR**0125433 (23:A2735)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0935104-2

Keywords:
Wiener measure,
Yeh-Wiener measure,
tight measure,
-parallel lines theorem,
converse measurability

Article copyright:
© Copyright 1988
American Mathematical Society