European Mathematical Society - m. m. rao
https://euro-math-soc.eu/author/m-m-rao
enConditional Measures and Applications, second edition
https://euro-math-soc.eu/review/conditional-measures-and-applications-second-edition
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This monograph presents a broad overview on conditioning with historical notes. It starts with principles, ideas and concepts for conditional probability measures. It then proceeds to a general concept based on conditional expectations that coincides with the Radon-Nikodým derivative. Some axiomatic definitions of conditioning are introduced. Later the conditional expectation is shown to be a particular case of a projection operator acting on functional spaces. The remaining theory, conditions and properties of conditioning are presented and discussed with several different backgrounds. The author is also interested in computational aspects of conditioning and in applications to mathematical statistics and random processes.<br />
One chapter is devoted to sufficient statistics, which are closely related or, more correctly, defined by means of conditioning. Later chapters deals with martingales, submartingales and Markov processes. For interested readers, the last two chapters describe the impact of conditioning on modern analysis and present conditioning concepts in general spaces as some subset of functions. The latter chapters give advanced reading on the subject from a general point of view. This comprehensive monograph on conditioning can be a valuable help for anyone interested in probability theory and the connection to abstract analysis. I recommend the book to any reader interested in probability and measure theory oriented to conditioning. The book will be convenient as a textbook for introductory, tutorial and advanced courses on conditioning.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">pl</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/m-m-rao" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">m. m. rao</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/chapman-hallcrc-boca-raton-pure-and-applied-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">chapman & hall/crc, boca raton: pure and applied mathematics</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2005</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">1-57444-593-6</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">USD 99,95</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/60-probability-theory-and-stochastic-processes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">60 Probability theory and stochastic processes</a></li></ul></span>Sat, 22 Oct 2011 18:50:00 +0000Anonymous40010 at https://euro-math-soc.euMeasure Theory and Integration, second edition
https://euro-math-soc.eu/review/measure-theory-and-integration-second-edition
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This monograph provides a significantly revised and expanded version of the original edition published in 1987 on the classical topics in measure theory and integration. The book starts with chapters on classical notions of measure theory (measurability, measure, measurable functions including sections on Lebesgue--Stieltjes measures, Carathéodory process, metric outer measures, or convergences of measures) and integration (abstract Lebesgue integration, convergence theorems, the Lp-spaces and the Vitali-Hahn-Saks theorem). Next chapters are devoted to differentiation and duality (the Hahn decomposition, the Radon-Nikodým theorem, dual spaces) and product measures and integrals. The material in the new chapter is concerned with the Henstock-Kurzweil nonabsolute integration, both on the real line and in Banach spaces.It follows an interesting chapter on analytic sets and Choquet's theory of capacities with an application to the Daniell integral. Last chapters treat materials on an elementary proof of the lifting theorem and on topological measures (the Riesz-Markov theorem, Haar measures). The final chapter is devoted to relations between abstract and topological measures. Each chapter is companioned by many exercises of varying difficulty which give further applications and extensions of the theory. The book is equipped with a bibliography (more than 170 references), list of standard symbols and notation and with the author and subject indices. The book is well understandable and requires only a basic knowledge of advanced calculus; moreover, some results from topology and set theory are collected in a short appendix, and also a section on basic cornerstones of Banach spaces is included. It can be warmly recommended to a broad spectrum of readers--to graduate students as well as young researches who wish to become acquainted with the basic elements and deeper properties of abstract analysis and its applications.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">jl</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/m-m-rao" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">m. m. rao</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/marcel-dekker-new-york-pure-and-applied-mathematics-vol-265" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">marcel dekker, new york: pure and applied mathematics, vol. 265</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2004</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">0-8247-5401-8 </div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">USD 195</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/28-measure-and-integration" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">28 Measure and integration</a></li></ul></span>Wed, 28 Sep 2011 15:06:05 +0000Anonymous39732 at https://euro-math-soc.eu