Comprising the major theorems of probability theory and the measure theoretical foundations of the subject, the main topics treated here are independence, interchangeability, and martingales. Particular emphasis is placed upon stopping times, both as tools in proving theorems and as objects of interest themselves. No prior knowledge of measure theory is assumed and a unique feature of the book is the combined presentation of measure and probability. It is easily adapted for graduate students familiar with measure theory using the guidelines given. Special features include: - A comprehensive treatment of the law of the iterated logarithm - The Marcinklewicz-Zygmund inequality, its extension to martingales and applications thereof - Development and applications of the second moment analogue of Walds equation - Limit theorems for martingale arrays; the central limit theorem for the interchangeable and martingale cases; moment convergence in the central limit theorem - Complete discussion, including central limit theorem, of the random casting of r balls into n cells - Recent martingale inequalities - Cram r-L vy theorem and factor-closed families of distributions.
This volume focuses on Sun Yat-sen's social, political, and economic ideas as seen in his major work, The Three Principles of the People, which discusses nationalism, democracy, and people's welfare, examining his doctrines as well as a his ideas with other contemporary ideologies.
Apart from new examples and exercises, some simplifications of proofs, minor improvements, and correction of typographical errors, the principal change from the first edition is the addition of section 9.5, dealing with the central limit theorem for martingales and more general stochastic arrays. vii Preface to the First Edition Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world. The origins of the sub ject, generally attributed to investigations by the renowned French mathe matician Fermat of problems posed by a gambling contemporary to Pascal, have been pushed back a century earlier to the Italian mathematicians Cardano and Tartaglia about 1570 (Ore, 1953). Results as significant as the Bernoulli weak law of large numbers appeared as early as 1713, although its counterpart, the Borel strong law oflarge numbers, did not emerge until 1909. Central limit theorems and conditional probabilities were already being investigated in the eighteenth century, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes (1921), von Mises (1928; 1931), and Kolmogorov (1933).
The 1989 prodemocracy movement in the People's Republic of China and the subsequent crackdown were marked by many dramatic reversals. Supported at first by several thousand Beijing University students, the movement quickly attracted millions of followers and developed into a nationwide mass movement. The jubilant mood during the short-lived freedom in Tiananmen Square turned into despair over the unnecessary bloodshed. The event raised many deeply disturbing questions: Was the massacre necessary and justified? What is the historical significance of this movement? Which path will the PRC follow in the decade ahead? Although no one had anticipated the tragic outcome, the popular unrest was not totally unexpected. When I read the news of 200,000 Beijing students and residents, in open defiance of the government's order, staging a largescale demonstration on Apri120, I knew a confrontation between the people and the government was inevitable.
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