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 This is a heretofore unpublished set of lecture notes by the late John von Neumann on invariant measures, including Haar measures on locally compact groups. The notes for the first half of the book have been prepared by Paul Halmos. The second half of the book includes a discussion of Kakutani's very interesting approach to invariant measures.

 The main purpose of this paper is to prove the existence, and in some cases the uniqueness, of unitarily invariant measures on formal completions of groups associated to affine Kac-Moody algebras, and associated homogeneous spaces. The basic invariant measure is a natural generalization of Haar measure for a simply connected compact Lie group, and its projection to flag spaces is a generalization of the normalized invariant volume element. The other invariant measures'' are actually measures having values in line bundles over these spaces; these bundle-valued measures heuristically arise from coupling the basic invariant measure to Hermitian structures on associated line bundles, but in this infinite dimensional setting they are generally singular with respect to the basic invariant measure.

 Exposed Points of Convex Sets and Weak Sequential Convergence has been writing in one form or another for most of life. You can find so many inspiration from Exposed Points of Convex Sets and Weak Sequential Convergence also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Exposed Points of Convex Sets and Weak Sequential Convergence book for free.

 Bulletin new Series of the American Mathematical Society has been writing in one form or another for most of life. You can find so many inspiration from Bulletin new Series of the American Mathematical Society also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Bulletin new Series of the American Mathematical Society book for free.

 Finitary Measures for Subshifts of Finite Type and Sofic Systems has been writing in one form or another for most of life. You can find so many inspiration from Finitary Measures for Subshifts of Finite Type and Sofic Systems also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Finitary Measures for Subshifts of Finite Type and Sofic Systems book for free.

 Conditional Stability and Real Analytic Pseudo Anosov Maps has been writing in one form or another for most of life. You can find so many inspiration from Conditional Stability and Real Analytic Pseudo Anosov Maps also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Conditional Stability and Real Analytic Pseudo Anosov Maps book for free.

 In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs («expanders»). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only ?nitely additive measure of total measure one, de?ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at ?rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan’s property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related.

 BPR has been writing in one form or another for most of life. You can find so many inspiration from BPR also informative, and entertaining. Click DOWNLOAD or Read Online button to get full BPR book for free.

 Convexity has been writing in one form or another for most of life. You can find so many inspiration from Convexity also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Convexity book for free.

 This concise classic by a well-known master of mathematical exposition covers recurrence, ergodic theorems, ergodicity and mixing properties, and the relation between conjugacy and equivalence. 1956 edition.

 Galois Theory Rings Algebraic Groups and Their Applications has been writing in one form or another for most of life. You can find so many inspiration from Galois Theory Rings Algebraic Groups and Their Applications also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Galois Theory Rings Algebraic Groups and Their Applications book for free.

 This volume contains papers based on lectures given at the 12th International Conference on p-adic Functional Analysis, which was held at the University of Manitoba on July 2-6, 2012. The articles included in this book feature recent developments in various areas of non-archimedean analysis: branched values and zeros of the derivative of a $p$-adic meromorphic function, p-adic meromorphic functions $f^{\prime}P^{\prime}(f), g^{\prime}P^{\prime}(g)$ sharing a small function, properties of composition of analytic functions, partial fractional differentiability, morphisms between ultrametric Banach algebras of continuous functions and maximal ideals of finite dimension, the $p$-adic $q$-distributions, Banach spaces over fields with an infinite rank valuation, Grobman-Hartman theorems for diffeomorphisms of Banach spaces over valued fields, integral representations of continuous linear maps on $p$-adic spaces of continuous functions, non-Archimedean operator algebras, generalized Keller spaces over valued fields, proper multiplications on the completion of a totally ordered abelian group, the Grothendieck approximation theory in non-Archimedean functional analysis, generalized power series spaces, measure theory and the study of power series and analytic functions on the Levi-Civita fileds. Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in non-archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.

 Library of Congress Catalogs has been writing in one form or another for most of life. You can find so many inspiration from Library of Congress Catalogs also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Library of Congress Catalogs book for free.

 Dorothy Maharam Stone's (1917-) contributions to operators and measure algebras has had a profound influence on this area of research. Her career, which has spanned nearly half a century, includes 40 research publications, some of them as recent as 1987. A Ph.D. student of Anna Pell Wheeler at Bryn Mawr College, Stone has been an active force in mathematics research and various professional activities.This volume contains the proceedings of the Conference on Measure and Measurable Dynamics, held in honor of Stone at the University of Rochester in September 1987. The papers in this collection represent contributions from some of the top experts in this field. Stone's work is surveyed in a number of articles which highlight her foundational results concerning positive operators, the characterization of homo-geneous measure algebras, and disintegrations. In addition, there are research papers in ergodic theory, measure theory, descriptive set theory, and the dynamics of measurable maps. A number of the results in these papers are directly related to Stone's work.