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Functions possessing restricted mean value properties. (English) Zbl 0251.31004

MSC:
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
60J45 Probabilistic potential theory
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[1] M. A. Akcoglu and R. W. Sharpe, Ergodic theory and boundaries, Trans. Amer. Math. Soc. 132 (1968), 447 – 460. · Zbl 0162.19402
[2] John R. Baxter, Restricted mean values and harmonic functions, Trans. Amer. Math. Soc. 167 (1972), 451 – 463. · Zbl 0238.31006
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[5] Марковские процессы, Государств. Издат. Физ.-Мат. Лит., Мосцощ, 1963 (Руссиан). · Zbl 0132.37701
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[7] W. A. Veech, The core of a measurable set and a problem in potential theory (preprint).
[8] William A. Veech, A converse to Gauss’ theorem, Bull. Amer. Math. Soc. 78 (1972), 444 – 446. · Zbl 0235.31013
[9] -, A zero-one law for a class of random walks and a converse to Gauss’ mean value theorem (preprint). · Zbl 0282.60048
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