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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
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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

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