Encyclopaedia of mathematics. Volume 9, Stochastic approximation - Zygmund class of functions : an updated and annotated translation of the Soviet 'Mathematical encyclopaedia'

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe­ matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi­ sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en­ gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques. The Indispensable Source of Information for all those who use Mathematics in Their Work ... This is undoubtedly the most comprehensive, up-to-date and authoritative mathematics encyclopaedia available today. Translated from the Russian, edited, annotated and updated by about 200 Western mathematicians, all specialists in their respective fields, the 10-volume Encyclopaedia of Mathematics contains nearly 7000 articles together with a wealth of complementary information. Explanations of differences in terminology are of historical interest and help to bridge the gap between Western and Soviet approaches to mathematics. The Encyclopaedia of Mathematics will help you: find the precise definition of a given concept loop up and verify terminology find the precise statement of a theorem reach the information you need via AMS classification number and/or keywords/phrases check the precise names of concepts and theorems find reference literature for a given field find out about applications of a concept and its links with other concepts This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics . This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available. This "Encyclopaedia of Mathematics" aims to be a reference work for all parts of mathematics. It is a translation with updates and editorial comments of the "Soviet Mathematical Encyclopaedia" published by the Soviet Encyclopaedia Publishing House in five volumes from 1977 to 1985. The annotated translation consists of ten volumes including a special index volume Front Matter....Pages i-ix S....Pages 1-121 T....Pages 123-300 U....Pages 301-356 V....Pages 357-437 W....Pages 439-512 Y....Pages 513-520 Z....Pages 521-536