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Bühlmann, H. Austauschbare stochastische Variabeln und ihre GrenzwertsÄtze. Univ. California Publ. Statist. 3, No. 1, 1–36 (1960).
Doob, J. L.: Stochastic processes. New York: John Wiley and Sons 1953.
Cramér, H.: über eine Eigenschaft der normalen Verteilungsfunktion. Math. Z. 41, 405–414 (1936).
Karhunen, K.: Zur Spektraltheorie stochastischer Prozesse. Ann. Acad. Sci. Fennicae. Ser. A. I. N. 34, 1–7 (1946).
Lévy, P.: Processus stochastiques et mouvement Brownien. Paris: Gauthier Villars 1948.
—: Sur les intégrales dont les éléments sont des variables aléatoires indépendantes. Ann. Scuola norm. sup. Pisa, 2nd Ser. 3, 337–366 (1934).
—: Le mouvement Brownien plan. Amer. J. Math. 62, 487–550 (1940).
Loève, M.: Fonctions aléatoires de second ordre. Rev. Sci. 83, 297–303 (1945) and Rev. Sci. 84, 195–206 (1946).
—: Probability Theory. 2nd edition. New York: Van Nostrand Co. 1960.
Raikov, D. A.: On a connection between the central limit theorem and the law of large numbers. (In Russian.) Izvestiya Akad. Nauk, SSSR, Ser. mat. 2, 323–338 (1950).
Wiener, N.: Harmonic analysis of irregular motion. J. Math. Physics 5, 99–121 and 158–190 (1925–26).
—: The quadratic variation of a function and its Fourier coefficients. J. Math. Physics 3, 72–94 (1924).
—: Note on a new type of summability. Amer. J. Math. 45, 83–86 (1923).
Zygmund, A.: Trigonometric Series. Vol. 1 and 2, 2nd edition. Cambridge Univ. Press 1959.
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Prepared with the partial support of the National Science Foundation, Grant G-14648.
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Bühlmann, H. L 2-martingales and orthogonal decomposition. Z. Wahrscheinlichkeitstheorie verw Gebiete 1, 394–414 (1963). https://doi.org/10.1007/BF00533415
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DOI: https://doi.org/10.1007/BF00533415