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100   $a20130430d2013      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aMeasure, Integral, Derivative $eA Course on Lebesgue's Theory /$fby Sergei Ovchinnikov
205   $a1st ed. 2013.
210  1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2013.
215   $a1 online resource (X, 146 p. 16 illus.) 
225 1 $aUniversitext,$x0172-5939
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a1-4614-7195-8 
320   $aIncludes bibliographical references (page 143) and index.
327   $a1 Preliminaries -- 2 Lebesgue Measure -- 3  Lebesgue Integration -- 4 Differentiation and Integration -- A Measure and Integral over Unbounded Sets -- Index.
330   $aThis classroom-tested text is intended for a one-semester course in Lebesgue?s theory.  With over 180 exercises, the text takes an elementary approach, making it easily accessible to both upper-undergraduate- and lower-graduate-level students.  The three main topics presented are measure, integration, and differentiation, and the only prerequisite is a course in elementary real analysis. In order to keep the book self-contained, an introductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results, such as the differentiability property of functions of bounded variations, are dissected into small steps in order to be accessible to students. With the exception of a few simple statements, all results are proven in the text.  The presentation is elementary, where ?-algebras are not used in the text on measure theory and Dini?s derivatives are not used in the chapter on differentiation. However, all the main results of Lebesgue?s theory are found in the book.
410  0$aUniversitext,$x0172-5939
606   $aMeasure theory
606   $aFunctions of real variables
606   $aMathematical analysis
606   $aAnalysis (Mathematics)
606   $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120
606   $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171
606   $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007
615  0$aMeasure theory.
615  0$aFunctions of real variables.
615  0$aMathematical analysis.
615  0$aAnalysis (Mathematics).
615 14$aMeasure and Integration.
615 24$aReal Functions.
615 24$aAnalysis.
676   $a515/.83
700   $aOvchinnikov$b Sergei$4aut$4http://id.loc.gov/vocabulary/relators/aut$0514053
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910438157203321
996   $aMeasure, integral, derivative$9821894
997   $aUNINA