Conditional independence. (English) Zbl 0363.60030


60F15 Strong limit theorems
60A05 Axioms; other general questions in probability
46B03 Isomorphic theory (including renorming) of Banach spaces
46B10 Duality and reflexivity in normed linear and Banach spaces
Full Text: DOI


[1] Beck, A.: Une loi forte des grands nombres dans des espaces de Banach uniformément convexes. Ann. Inst. H. Poincaré 16, 35-45 (1958) · Zbl 0131.35306
[2] Beck, A.: A convexity condition in Banach spaces and the strong law of large numbers. Proc. Amer. Math. Soc. 13, 329-334 (1962) · Zbl 0108.31401
[3] Beck, A.: On the strong law of large numbers, Chapter of Ergodic Theory. F.B. Wright, ed. New York: Academic Press 1963 · Zbl 0132.13001
[4] Beck, A., Giesy, D.P.: P-uniform convergence and a vector-valued strong law of large numbers. Trans. Amer. Math. Soc. 147, 541-559 (1970) · Zbl 0198.51006
[5] Beck, A., Warren, P.: Weak orthogonality. Pacific J. Math. 41, 1-11 (1972) · Zbl 0243.46044
[6] Beck, A., Warren, P.: Strong laws of large numbers for weakly orthogonal sequences of Banach space-valued random variables. Ann. Probability 2, 918-925 (1974) · Zbl 0293.60026
[7] Beck, A., Warren, P.: Coubter examples to strong laws of large numbers for Banach space-valued random variables. University of Denver preprints (1974) · Zbl 0293.60026
[8] Feller, W.: An Introduction to Probability Theory and its Applications Vol. II. New York: Wiley 1966 · Zbl 0138.10207
[9] Giesy, D.P.: On a convexity condition in normed linear spaces. Trans. Amer. Math. Soc. 125, 114-116 (1966) · Zbl 0183.13204
[10] Hille, E., Phillips, R.S.: Functional Analysis and Semi-groups (Revised edition). Amer. Math. Soc. Colloq. Publ. 31, Providence, R.I. (1957) · Zbl 0078.10004
[11] Mourier, E.: Elements Aléatoires dans un espace de Banach. Ann. Inst. H. Poincaré 13, 159-244 (1953) · Zbl 0053.09503
[12] Padgett, W.J., Taylor, R.L.: Laws of Large Numbers for Normed Linear Spaces and Certain Fréchet Spaces. Lecture Notes in Math. 360, Berlin-Heidelberg-New York: Springer 1973 · Zbl 0275.60010
[13] Pettis, B.J.: On integration in vector space. Trans. Amer. Math. Soc. 44, 277-304 (1938) · Zbl 0019.41603
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