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References
Baxter, G.: A general ergodic theorem with weighted averages. J. Math. Mech. 14, 277–288 (1965)
Beck, A., Schwartz, J.T.: A vector-valued random ergodic theorem. Proc. Amer. Math. Soc. 8, 1049–1059 (1957)
Bochner, S.: Integration von Funktionen, deren Werte die Elemente eines Vektorraumes sind. Fund. Math. 20, 262–276 (1933)
Cairoli, R.: Sur le théorème ergodique aléatoire. Bull. Sci. Math. 88, 31–37 (1964)
Chacon, R.V.: An ergodic theorem for operators satisfying norm conditions. J. Math. Mech. 11, 165–172 (1962)
Chacon, R.V.: Convergence of operator averages. Ergodic Theory (ed. by F.B. Wright), 89–120. New York: Academic Press 1963
Chacon, R.V.: Ordinary means imply recurrent means. Bull. Amer. Math. Soc. 70, 796–797 (1964)
Dowker, Y.N.: A new proof of the general ergodic theorem. Acta Sci. Math. (Szeged) 12, 162–166 (1950)
Dunford, N., Miller, D.S.: On the ergodic theorem. Trans. Amer. Math. Soc. 60, 538–549 (1946)
Feller, W.: An introduction to probability theory and its applications. Vol. I, 2nd Ed. New York: Wiley 1957
Gladysz, S.: über den stochastischen Ergodensatz. Studia Math. 15, 158–173 (1956)
Halmos, P.R.: An ergodic theorem. Proc. Nat. Acad. Sci. U.S.A. 32, 156–161 (1946)
Hille, E, Phillips, R.S.: Functional analysis and semigroups. Colloq. Publ. Amer. Math. Soc. 1957
Hopf, E.: Ergodentheorie. Berlin: Springer 1937
Hurewicz, W.: Ergodic theorems without invariant measure. Ann. Math. 45, 192–206 (1944)
Kin, E.: Skew products of dynamical systems. Trans. Amer. Math. Soc. 166, 27–43 (1972)
Révész, P.: A random ergodic theorem and its application to the theory of Markov chains. Ergodic Theory (F.B. Wright, ed.), 217–250. New York: Academic Press 1963
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Yoshimoto, T. Random ergodic theorem with weighted averages. Z. Wahrscheinlichkeitstheorie verw Gebiete 30, 149–165 (1974). https://doi.org/10.1007/BF00532267
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DOI: https://doi.org/10.1007/BF00532267