Journal of Theoretical Probability

, Volume 3, Issue 4, pp 489–496

The decomposition theorem for functions satisfying the law of large numbers

  • V. Dobric

DOI: 10.1007/BF01046091

Cite this article as:
Dobric, V. J Theor Probab (1990) 3: 489. doi:10.1007/BF01046091


LetB be a Banach space with the Radon-Nikodym property and (S, ϕ, μ) a probability space. Then anf: S→B satisfies the strong law of large numbers if and only if there exists a Bochner integrable functionf1 and a Pettis integrable functionf2,f2f2‖=0 in the Glivenko-Cantelli norm, such thatf=f1+f2. The composition is unique.

Key words

Banach spaces with the Radon-Nikodym property the strong law of large numbers compact operators 

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • V. Dobric
    • 1
  1. 1.Department of MathematicsLehigh UniversityBethlehem

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