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Proceedings of the American Mathematical Society

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


Author: Robert C. Stolz
Journal: Proc. Amer. Math. Soc. 125 (1997), 1215-1220
MSC (1991): Primary 60B12
DOI: https://doi.org/10.1090/S0002-9939-97-03686-1
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: https://doi.org/10.1090/S0002-9939-97-03686-1
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. Dobrić during a stay at Lehigh University.
Communicated by: Richard T. Durrett
Article copyright: © Copyright 1997 American Mathematical Society