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Best measure kolmogorov reviews

1. Selected Works of A.N. Kolmogorov: vol. 2 Probability Theory and Mathematical Statistics

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Used Book in Good Condition

Description

The creative work of Andrei N. Kolmogorov is exceptionally wide-ranging. In his studies on trigonometric and orthogonal series, the theory of measure and integral, mathematical logic, approximation theory, geometry, topology, functional analysis, classical mechanics, ergodic theory, superposition of functions, and in formation theory, he solved many conceptual and fundamental problems and posed new questions which gave rise to a great deal of further research. Kolmogorov is one of the founders of the Soviet school of probability theory, mathematical statistics, and the theory of turbulence. In these areas he obtained a number of central results, with many applications to mechanics, geophysics, linguistics and biology, among other subjects. This edition includes Kolmogorov's most important papers on mathematics and the natural sciences. It does not include his philosophical and pedagogical studies, his articles written for the "Bolshaya Sovetskaya Entsiklopediya", his papers on prosody and applications of mathematics or his publications on general questions. The material of this edition was selected and compiled by Kolmogorov himself.

The first volume consists of papers on mathematics and also on turbulence and classical mechanics. The second volume is devoted to probability theory and mathematical statistics. The focus of the third volume is on information theory and the theory of algorithms.


2. Introductory Real Analysis (Dover Books on Mathematics)

Description

This volume in Richard Silverman's exceptional series of translations of Russian works in the mathematical science is a comprehensive, elementary introduction to real and functional analysis by two faculty members from Moscow University. It is self-contained, evenly paced, eminently readable, and readily accessible to those with adequate preparation in advanced calculus.
The first four chapters present basic concepts and introductory principles in set theory, metric spaces, topological spaces, and linear spaces. The next two chapters consider linear functionals and linear operators, with detailed discussions of continuous linear functionals, the conjugate space, the weak topology and weak convergence, generalized functions, basic concepts of linear operators, inverse and adjoint operators, and completely continuous operators. The final four chapters cover measure, integration, differentiation, and more on integration. Special attention is here given to the Lebesque integral, Fubini's theorem, and the Stieltjes integral. Each individual section there are 37 in all is equipped with a problem set, making a total of some 350 problems, all carefully selected and matched.
With these problems and the clear exposition, this book is useful for self-study or for the classroom it is basic one-year course in real analysis. Dr. Silverman is a former member of the Institute of Mathematical Sciences of New York University and the Lincoln Library of M.I.T. Along with his translation, he has revised the text with numerous pedagogical and mathematical improvements and restyled the language so that it is even more readable.

3. Elements of the Theory of Functions and Functional Analysis (Dover Books on Mathematics)

Description

Originally published in two volumes, this advanced-level text is based on courses and lectures given by the authors at Moscow State University and the University of Moscow.
Reprinted here in one volume, the first part is devoted to metric and normal spaces. Beginning with a brief introduction to set theory and mappings, the authors offer a clear presentation of the theory of metric and complete metric spaces. The principle of contraction mappings and its applications to the proof of existence theorems in the theory of differential and integral equations receives detailed analysis, as do continuous curves in metric spaces a topic seldom discussed in textbooks.
Part One also includes discussions of other subjects, such as elements of the theory of normed linear spaces, weak sequential convergence of elements and linear functionals, adjoint operators, and linear operator equations. Part Two focuses on an exposition of measure theory, the Lebesque interval and Hilbert Space. Both parts feature numerous exercises at the end of each section and include helpful lists of symbols, definitions, and theorems.

4. The Measure of All Minds: Evaluating Natural and Artificial Intelligence

Description

Are psychometric tests valid for a new reality of artificial intelligence systems, technology-enhanced humans, and hybrids yet to come? Are the Turing Test, the ubiquitous CAPTCHAs, and the various animal cognition tests the best alternatives? In this fascinating and provocative book, Jos Hernndez-Orallo formulates major scientific questions, integrates the most significant research developments, and offers a vision of the universal evaluation of cognition. By replacing the dominant anthropocentric stance with a universal perspective where living organisms are considered as a special case, long-standing questions in the evaluation of behavior can be addressed in a wider landscape. Can we derive task difficulty intrinsically? Is a universal g factor - a common general component for all abilities - theoretically possible? Using algorithmic information theory as a foundation, the book elaborates on the evaluation of perceptual, developmental, social, verbal and collective features and critically analyzes what the future of intelligence might look like.

5. Measures of Complexity: Festschrift for Alexey Chervonenkis

Description

This book brings together historical notes, reviews of research developments, fresh ideas on how to make VC (VapnikChervonenkis) guarantees tighter, and new technical contributions in the areas of machine learning, statistical inference, classification, algorithmic statistics, and pattern recognition.

The contributors are leading scientists in domains such as statistics, mathematics, and theoretical computer science, and the book will be of interest to researchers and graduate students in these domains.

6. An Introduction to the Kolmogorov-Bernoulli Equivalence (SpringerBriefs in Mathematics)

Description

This book offers an introduction to a classical problem in ergodic theory and smooth dynamics, namely, the KolmogorovBernoulli(non)equivalence problem, and presents recent results in this field. Starting with a crash course on ergodic theory, it uses the class of ergodic automorphisms of the two tori as a toy model to explain the main ideas and technicalities arising in the aforementioned problem. The level of generality then increases step by step, extending the results to the class of uniformly hyperbolic diffeomorphisms, and concludes with a survey of more recent results in the area concerning, for example, the class of partially hyperbolic diffeomorphisms. It is hoped that with this type of presentation, nonspecialists and young researchers in dynamical systems may be encouraged to pursue problems in this area.



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