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

Stolz, Robert

doi:10.1090/S0002-9939-97-03686-1

The structure of functions satisfying the law of large numbers in a class of locally convex spaces
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by Robert C. Stolz

Proc. Amer. Math. Soc. 125 (1997), 1215-1220

DOI: https://doi.org/10.1090/S0002-9939-97-03686-1

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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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