Description
This book is about metric number theory and it covers a lot of different topics. It starts with classical results from Borel, Khintchine, and Weyl and then goes on to discuss more general questions. It also covers topics like normal numbers, Diophantine approximation, and uniform distribution. Finally, it discusses some dimensions of sets that are special in the sense that they have zero measure.
This book deals with the number-theoretic properties of almost all real numbers. It brings together many different types of result never covered within the same volume before, thus showing interactions and common ideas between different branches of the subject. It provides an indispensable compendium of basic results, important theorems and open problems. Starting from the classical results of Borel, Khintchine and Weyl, normal numbers, Diophantine approximation and uniform distribution are all discussed. Questions are generalized to higher dimensions and various non-periodic problems are also considered (for example restricting approximation to fractions with prime numerator and denominator). Finally, the dimensions of some of the exceptional sets of measure zero are considered. Review: ...very interesting book... Peter Szusz, Zentralblatt MATH, Vol 1081
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