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Invariant means and conditional expectation operators

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Abstract

We investigate the possibility of an integral representation of conditional expectation operators. We give conditions for an integral representation of conditional expectation operators with respect to the σ-algebra of G-invariant sets, where G is an amenable group of automorphisms of a probability space, corresponding to some partition of the space by trajectories.

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Literature cited

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Authors
  1. V. G. Kulakova
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 73, pp. 207–210, 1977.

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Kulakova, V.G. Invariant means and conditional expectation operators. J Math Sci 34, 2146–2148 (1986). https://doi.org/10.1007/BF01741590

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  • DOI: https://doi.org/10.1007/BF01741590

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