On a measure in Wiener space and applications

Authors:
K. S. Ryu and M. K. Im

Journal:
Trans. Amer. Math. Soc. **355** (2003), 2205-2222

MSC (2000):
Primary 28C20, 44A15, 46G12, 46T12, 58D20

DOI:
https://doi.org/10.1090/S0002-9947-03-03190-8

Published electronically:
February 4, 2003

MathSciNet review:
1973988

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this article, we consider a measure in Wiener space, induced by the sum of measures associated with an uncountable set of positive real numbers, and investigate the basic properties of this measure. We apply this measure to the various theories related to Wiener space. In particular, we can obtain a partial answer to Johnson and Skoug's open problems, raised in their 1979 paper. Moreover, we can improve and clarify some theories related to Wiener space.

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Additional Information

**K. S. Ryu**

Affiliation:
Department of Mathematics, Han Nam University, Taejon 306-791, Korea

Email:
ksr@math.hannam.ac.kr

**M. K. Im**

Affiliation:
Department of Mathematics, Han Nam University, Taejon 306-791, Korea

Email:
mki@mail.hannam.ac.kr

DOI:
https://doi.org/10.1090/S0002-9947-03-03190-8

Keywords:
Wiener measure,
scale-invariant measurability,
Fourier-Feynman transform

Received by editor(s):
April 6, 2001

Received by editor(s) in revised form:
August 29, 2002

Published electronically:
February 4, 2003

Additional Notes:
This work was supported by grant No. 2001-1-10100-011-1 from the Basic Research Program of the Korea Science $&$ Engineering Foundation.

Article copyright:
© Copyright 2003
American Mathematical Society