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A Local Ergodic Theorem for Multiparameter Superadditive Processes

Published online by Cambridge University Press:  20 November 2018

Ryotaro Sato*
Affiliation:
Department of mathematics Faculty of science, Okayama UniversityOkayama, 700Japan
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Abstract

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In this paper a local ergodic theorem is proved for positive (multiparameter) superadditive processes with respect to (multiparameter) semiflows of nonsingular point transformations on a a-finite measure space. The theorem obtained here generalizes Akcoglu-Krengel's [2] local ergodic theorem for superadditive processes with respect to semiflows of measure preserving transformations. The proof is a refinement of Akcoglu-Krengel's argument in [2]. Also, ideas of Feyel [3] and the author [4], [5] are used.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Akcoglu, M.A. and A. del Junco, Differentiation of n-dimensional additive processes, Canad. J. Math. 33 (1981), pp. 749768.Google Scholar
2. Akcoglu, M.A. and Krengel, U., Ergodic theorems for superadditive processes, J. Reine Angew. Math. 323 (1981), pp. 5367.Google Scholar
3. Feyel, D., Convergence locale des processus sur-abéliens et sur-additifs, C. R. Acad. Sci. Paris, Sér. I, 295 (1982), pp. 301303.Google Scholar
4. Sato, R., On local ergodic theorems for positive semigroups, Studia Math. 63 (1978), pp. 45—55.Google Scholar
5. Sato, R., On local properties of k-parameter semiflows of nonsingular point transformations, Acta Math. Hung, (to appear).Google Scholar
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