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ISSN 1088-6826(e) ISSN 0002-9939(p)

The structure of functions satisfying the law of large numbers in a class of locally convex spaces

Author(s): Robert C. Stolz
Journal: Proc. Amer. Math. Soc. 125 (1997), 1215-1220.
MSC (1991): Primary 60B12
MathSciNet review: 1363187
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Abstract: For each function $f$ that satisfies the law of large numbers with values in a certain class of locally convex spaces with the Radon-Nikodym property the following decomposition holds: $f=f_1+f_2$ , where $f_1$ is integrable by seminorm, and $f_2$ is a Pettis integrable function which is scalarly 0.

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Additional Information:

Robert C. Stolz
Affiliation: Department of Mathematics, Lafayette College, Easton, Pennsylvania 18042
Address at time of publication: Division of Science and Mathematics, University of the Virgin Islands, St. Thomas, Virgin Islands 00802
Email: StolzR@lafayette.edu, Robert.Stolz@uvi.edu

DOI: 10.1090/S0002-9939-97-03686-1
PII: S 0002-9939(97)03686-1
Keywords: The law of large numbers, locally convex spaces
Received by editor(s): July 14, 1995
Received by editor(s) in revised form: October 10, 1995
Additional Notes: The present paper is part of the author's doctoral thesis and was carried out under the supervision of Professor V. Dobric during a stay at Lehigh University.
Communicated by: Richard T. Durrett
Copyright of article: Copyright 1997, American Mathematical Society

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