浙江大学的林正炎教授和东北师范大学的白志东教授编著的 Probability Inequality, 2009年，Science Press Bejing 和 Springer联合出版。
     In almost every branch of quantitative sciences, inequalities play an important role in its development and are regarded to be even more important than equalities. This is indeed the case in probability and statistics. For example, the Chebyshev, Schwarz and Jensen inequalities are frequently used in probability theory, the Cramer-Rao inequality plays a fundamental role in mathematical statistics. Choosing or establishing an appropriate inequality is usually a key breakthrough in the solution of a problem, e.g. the Berry-Esseen inequality opens a way to evaluate the convergence rate of the normal approximation.
    Research beginners usually face two difficulties when they start researching—they choose an appropriate inequality and/or cite an exact reference. In literature, almost no authors give references for frequently used inequalities, such as the Jensen inequality, Schwarz inequality, Fatou Lemma, etc. Another annoyance for beginners is that an inequality may have many different names and reference sources. For example, the Schwarz inequality is also called the Cauchy, Cauchy-Schwarz or Minkovski-Bnyakovski inequality. Bennet, Hoeffding and Bernstein inequalities have a very close relationship and format, and in literature some authors cross-cite in their use of the inequalities. This may be due to one author using an inequality and subsequent authors just simply copying the inequality’s format and its reference without checking the original reference. All this may distress beginners very much.
    The aim of this book is to help beginners with these problems. We provide a place to find the most frequently used inequalities, their proofs (if not too lengthy) and some references. Of course, for some of the more popularly known inequalities, such as Jensen and Schwarz, there is no necessity to give a reference and we will not do so. The wording “frequently used” is based on our own understanding. It can be expected that many important probability inequalities are not collected in this work. Any comments and suggestions will be appreciated.

    The writing of the book is supported partly by the National Science Foundation of China.

    The authors would like to express their thanks to Ron Lim Beng Seng for improving our English in this book.

Zhengyan Lin
May, 2009