LEADER 04592nam 22006135 450 001 9910299989903321 005 20250609110745.0 010 $a1-4939-1841-9 024 7 $a10.1007/978-1-4939-1841-6 035 $a(CKB)3710000000306065 035 $a(SSID)ssj0001386357 035 $a(PQKBManifestationID)11809737 035 $a(PQKBTitleCode)TC0001386357 035 $a(PQKBWorkID)11374004 035 $a(PQKB)10949356 035 $a(DE-He213)978-1-4939-1841-6 035 $a(MiAaPQ)EBC6310654 035 $a(MiAaPQ)EBC5594778 035 $a(Au-PeEL)EBL5594778 035 $a(OCoLC)1076232954 035 $a(PPN)183088654 035 $a(MiAaPQ)EBC2000718 035 $a(EXLCZ)993710000000306065 100 $a20141115d2014 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aBasic Real Analysis /$fby Houshang H. Sohrab 205 $a2nd ed. 2014. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Birkhäuser,$d2014. 215 $a1 online resource (XI, 683 p. 3 illus.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a1-4939-1840-0 327 $aPreface -- Set Theory -- Sequences and Series of Real Numbers -- Limits of Functions -- Topology of R and Continuity -- Metric Spaces -- The Derivative -- The Riemann Integral -- Sequences and Series of Functions -- Normed and Function Spaces -- The Lebesgue Integral -- Lebesgue Measure -- General Measure and Probability -- Appendix A: Construction of Real Numbers -- References -- Index. 330 $aThis expanded second edition presents the fundamentals and touchstone results of real analysis in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. The text is a comprehensive and largely self-contained introduction to the theory of real-valued functions of a real variable. The chapters on Lebesgue measure and integral have been rewritten entirely and greatly improved. They now contain Lebesgue?s differentiation theorem as well as his versions of the Fundamental Theorem(s) of Calculus. With expanded chapters, additional problems, and an expansive solutions manual, Basic Real Analysis, Second Edition, is ideal for senior undergraduates and first-year graduate students, both as a classroom text and a self-study guide. Reviews of first edition: The book is a clear and well-structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. The prerequisites are few, but a certain mathematical sophistication is required. ... The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact, this textbook can serve as a source of examples and exercises in real analysis. ?Zentralblatt MATH The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest. ?Mathematical Reviews [This text] introduces upper-division undergraduate or first-year graduate students to real analysis.... Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear. ?CHOICE Reviews. 606 $aMeasure theory 606 $aLogic, Symbolic and mathematical 606 $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120 606 $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005 615 0$aMeasure theory. 615 0$aLogic, Symbolic and mathematical. 615 14$aMeasure and Integration. 615 24$aMathematical Logic and Foundations. 676 $a510 700 $aSohrab$b Houshang H$4aut$4http://id.loc.gov/vocabulary/relators/aut$0722026 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299989903321 996 $aBasic real analysis$91410130 997 $aUNINA