Almost Everywhere Convergence II. Proceedings of the by Alexanra Bellow, Alexandra Bellow, Roger L. Jones PDF

By Alexanra Bellow, Alexandra Bellow, Roger L. Jones

ISBN-10: 0120855208

ISBN-13: 9780120855209

Virtually all over the place Convergence II comprises chosen papers shape the second one overseas convention on virtually all over convergence in likelihood and Ergodic idea, which happened on October 16-20, 1989 at Northwestern college. It comprises survey papers and significant unique contributions and may entice researchers within the sector of ergodic thought and harmonic research in addition to to graduate scholars coming into those fields of analysis

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Extra resources for Almost Everywhere Convergence II. Proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, Evanston, Illinois, October 16–20, 1989

Example text

B above. 3) (Bk)keN and (Ajt(r))jteiv be two sequences in 1R* such that Σ Etf) and A,(r) > £ Bt> i€J(*) E\^\r for all t € JV \ {1}. i€J(/) To ease the intuitive understanding of the conditions appearing below, we recall that in the "classical" case (a^j^n (2*- 1 , 2 ' ] n W , and A = = (j)j^N one can choose i/(£) := 2 / , J(t) := N\{1}. The main result of this paper is the following extension of Theorem 6 in Fuk and Nagaev [4]. (Cf. 1. 4) ΣΡ{\\Χί\\>6&}<οο; ... 7) limsupai^llS^/ail^ll <^-})|| <7.

As the sequence {na} is dense in [0,1) (mod 1) we can inductively find integers K < nt < n2 < ··· < n m such that (1) nka € ( - a t l - a t + ß/A) (mod 1). Call N = n m . /(4N)f and let (3) c = [K/ 7 ] be the integral part of K/7. Note that since K/7 — 1 < c < K/7 we have (4) K - l < K - 7 < c7 < K and hence (5) /3cT < i K = i = e. Let now p G N and F = p+c-1 U [i-f a, i + a + 7). i= p Define Αλ = [Ο,β) x F and ϊι = 1 A . c7 < €. For each CJ € Ω there is an integer k with 1 < k < m and ω 6 [a t ,b t ).

B. Marcus, (-radial Processes and Random Fourier Series, Memoirs Amer. Math. Soc. , 1987. 39 18. K. Petersen, Another proof of the existence of the ergodic Hubert transform, Proc. Amer. Math. Soc. 88 (1983), 39-43. 19. H. , 1989. Department of Mathematics CB#3250, Phillips Hall University of North Carolina Chapel Hill, NC 27599 USA 40 On Hopfs Ergodic Theorem for Particles with Different Velocities by 1 Alexandra Bellow and Ulrich Krengel2 Summary In 1936 E. Hopf [H2] answered a limiting problem on the distribution of a cloud of particles in a box with the help of a general L r mean ergodic theorem.

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Almost Everywhere Convergence II. Proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, Evanston, Illinois, October 16–20, 1989 by Alexanra Bellow, Alexandra Bellow, Roger L. Jones


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