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On the convergence of a bounded amart and a conjecture of Chatterji

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  • Schmidt, Klaus D.

Abstract

Through the decomposition theorem of Lebesgue and Darst it is possible to define a generalized Radon-Nikodym derivative of a bounded additive set function with respect to a bounded countably additive set function. For a bounded amart the derivatives of the components are shown to converge almost everywhere. This result, together with a characterization of amarts, yields a theorem stated by Chatterji whose proof is incorrect.

Suggested Citation

  • Schmidt, Klaus D., 1981. "On the convergence of a bounded amart and a conjecture of Chatterji," Journal of Multivariate Analysis, Elsevier, vol. 11(1), pages 58-68, March.
    • Handle: RePEc:eee:jmvana:v:11:y:1981:i:1:p:58-68
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