Classroom notes of Cramer's lectures in Princeton (2 folders). 1946

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Material Information

Title:
Classroom notes of Cramer's lectures in Princeton (2 folders). 1946
Physical Description:
Unknown
Language:
English
Creator:
Chung, Kai Lai
Physical Location:
Box: 2
Folder: Classroom notes of Cramer's lectures in Princeton (2 folders). 1946

Subjects

Subjects / Keywords:
Mathematics -- History -- 20th century

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
System ID:
AA00007276:00001

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    By Kai-dai Ohung and Paul Erdos

    1. Let X ., 3 rs... '. independent random Variables and let 8 *

    A-1In the so-called "3, of the iteryt- logarithlm', completely 'as ve by Feller recent-

    p .upper limit of f as n is ooasiderpt and.its trub oerar of magnitude%
    a-,, is found with probability one, A .mntoirmprt to thpt problem It to consider the

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    The lower limit was actually considered together with the upper liJit by stein-
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    An apparent reason is perhaps the following. While the simplest special case

    (Itm) with pa4/2 .u.ready yiedsa a result which indicates the general form of the

    solution in the problem of lir 8 this special case becomes "degenerate" in the

    problem of lim In fact It is well-known ) that in this case and also i'n the

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    (1.8) Pr( 8 -npO infinitely often )-L.

    Now if p is irrational S can never vanish, however it is well-known ) that

    with probability one it aeh&nas sign infinitely often. The question naturally

    arises as to how close it can oone near Sero. An answer to this question is given

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