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GALAMBOS, J. and SIMONELLI, G. Bonferroni-type Inequalities with Applications. Springer-Verlag, New York, 1996. ix + 269 pp. $54.95/.34.00/DM88.00. ISBN 0-387-94776-0.
The authors provide an interesting and comprehensive description of Bonferroni-type inequalities, which cover many diverse fields of research and applications. Under this general heading many inequalities have been grouped, including the simple Bonferroni inequality. These inequalities are useful for obtaining asymptotic results for limit theorems and for bounding unknown quantities and, as such, they have found a plethora of applications in many scientific fields. The authors have gathered together a large number of such inequalities appearing in statistics, number theory, linear programming, and combinatorics. The appealing aspect of this book is the unifying approach in the presentation of all these results and their treatment from several different points of view.
The book is well organised into chapters. In the General Introduction some simple inequalities are reported, motivating the subsequent analysis....