9 pages matching Levy's theorem in this book
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B-measurable function B-measurable mapping belongs to d.-class Borel field Borel set Borel subsets bounded function brownian motion called cN(u completely additive class conditional probability law continuous convolution define J fdq denote DX(t easily verified elementary set existence and uniqueness f fdp Feller finite Fokker-Plank equation fonctions aleatoires fundamental differential process Gaussian distribution Gh(u implies independent infinitely divisible law interval N,N l.i.P. J fdp Lemma Let y(t Levy's theorem limit in probability logarithmic characteristic function Math n(du obtain Theorem open set probability distribution prove the existence purely discontinuous random variable recursively regular kernel sequence Similarly simple Markoff process Slutsky solution of 11.7 stochastic differential equation stochastic integral equation stochastic process sufficiently large system of probability Theorem 11 Theorem 2.2 three elements totally bounded transition probability law uniformly convergent uniformly stepwise function whole space Wiener's integral