{"product_id":"real-analysis-measure-and-integration-paperback","title":"Real Analysis: Measure and Integration - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eMarat V. Markin\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe philosophy of the book, which makes it quite distinct from many existing texts on the subject, is based on treating the concepts of measure and integration starting with the most general abstract setting and then introducing and studying the Lebesgue measure and integration on the real line as an important particular case. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eThe book consists of \u003cem\u003enine chapters\u003c\/em\u003e and \u003cem\u003eappendix, \u003c\/em\u003e with the material flowing from the \u003cem\u003ebasic set classes\u003c\/em\u003e, through \u003cem\u003emeasures\u003c\/em\u003e, \u003cem\u003eouter measures \u003c\/em\u003eand the general procedure of \u003cem\u003emeasure extension, \u003c\/em\u003ethrough \u003cem\u003emeasurable functions\u003c\/em\u003e and \u003cem\u003evarious types of convergence \u003c\/em\u003eof sequences of such based on the idea of measure, to the fundamentals of the abstract Lebesgue integration, the basic \u003cem\u003elimit theorems\u003c\/em\u003e, and the comparison of the Lebesgue and Riemann integrals. Also, studied are \u003cem\u003eLp spaces, \u003c\/em\u003ethe basics of normed vector spaces, and \u003cem\u003esigned \u003c\/em\u003e\u003cem\u003emeasures\u003c\/em\u003e. The novel approach based on the Lebesgue measure and integration theory is applied to develop a better understanding of differentiation and extend the classical \u003cem\u003etotal change formula \u003c\/em\u003elinking differentiation with integration to a substantially wider class of functions. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eBeing designed as a text to be used in a classroom, the book constantly calls for the student's actively mastering the knowledge of the subject matter. There are problems at the end of each chapter, starting with Chapter 2 and totaling at 125. Many important statements are given as problems and frequently referred to in the main body. There are also 358 Exercises throughout the text, including Chapter 1 and the Appendix, which require of the student to prove or verify a statement or an example, fill in certain details in a proof, or provide an intermediate step or a counterexample. They are also an inherent part of the material. More difficult problems are marked with an asterisk, many problems and exercises are supplied with   existential'' hints. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eThe book is generous on Examples and contains numerous Remarks accompanying definitions, examples, and statements to discuss certain subtleties, raise questions on whether the converse assertions are true, whenever appropriate, or whether the conditions are essential. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eWith\u003cem\u003e \u003c\/em\u003eplenty of examples, problems, and exercises, this well-designed text is ideal for a one-semester Master's level graduate course on real analysis with emphasis on the measure and integration theory for students majoring in mathematics, physics, computer science, and engineering. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\u003cstrong\u003e\u003c\/strong\u003e \u003cul\u003e \u003cli\u003eA concise but profound and detailed presentation of the basics of real analysis with emphasis on the measure and integration theory.\u003c\/li\u003e \u003cli\u003eDesigned for a one-semester graduate course, with plethora of examples, problems, and exercises.\u003c\/li\u003e \u003cli\u003eIs of interest to students and instructors in mathematics, physics, computer science, and engineering. \u003c\/li\u003e \u003cli\u003ePrepares the students for more advanced courses in functional analysis and operator theory. \u003c\/li\u003e \u003cp\u003e\u003c\/p\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003cstrong\u003eContents\u003cbr\u003e\u003c\/strong\u003ePreliminaries\u003cbr\u003eBasic Set Classes\u003cbr\u003eMeasures\u003cbr\u003eExtension of Measures\u003cbr\u003eMeasurable Functions\u003cbr\u003eAbstract Lebesgue Integral\u003cbr\u003e\u003cem\u003eLp\u003c\/em\u003e Spaces\u003cbr\u003eDifferentiation and Integration\u003cbr\u003eSigned Measures\u003cbr\u003eThe Axiom of Choice and Equivalents\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003cstrong\u003eMarat V. Markin\u003c\/strong\u003e, California State University, Fresno, USA.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 354\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.9 x 9.4 x 6.6 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e June 17, 2019\u003c\/div\u003e\n            ","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":43152498556991,"sku":"9783110600971","price":111.59,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0105\/8226\/1823\/files\/syHCSHAHcQ9783110600971_4b19d90c-d929-4d4c-825d-c110ca5f591e.jpg?v=1776937934","url":"https:\/\/dhlswag.com\/products\/real-analysis-measure-and-integration-paperback","provider":"BBB","version":"1.0","type":"link"}