LEADER 03978nam 22006015 450 001 9910983484303321 005 20250806173610.0 010 $a9789819725113 024 7 $a10.1007/978-981-97-2511-3 035 $a(CKB)37312840200041 035 $a(MiAaPQ)EBC31885443 035 $a(Au-PeEL)EBL31885443 035 $a(DE-He213)978-981-97-2511-3 035 $a(EXLCZ)9937312840200041 100 $a20250121d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMeasure and Integration $eAn Introduction /$fby Satya N. Mukhopadhyay, Subhasis Ray 205 $a1st ed. 2025. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2025. 215 $a1 online resource (647 pages) 225 1 $aUniversity Texts in the Mathematical Sciences,$x2731-9326 311 08$a9789819725106 327 $aPreliminaries -- Lebesgue Measure on Real Line -- Measurable Functions -- More about Sets and Functions -- The Lebesgue Integral -- Differentiation of Functions -- Lebesgue measure and integration in RN -- General Measure and Outer Measure -- Function Spaces -- Signed Measure and Complex Measure. 330 $aDesigned for senior undergraduate and graduate students in mathematics, this textbook offers a comprehensive exploration of measure theory and integration. It acts as a pivotal link bridging the Riemann integral and the Lebesgue integral, with a primary focus on tracing the evolution of measure and integration from their historical roots. A distinctive feature of the book is meticulous guidance, providing a step-by-step journey through the subject matter, thus rendering complex concepts more accessible to beginners. A fundamental grasp of differential and integral calculus, as well as Riemann integration, is recommended to ensure a smoother comprehension of the material. This textbook comprises 10 well-structured chapters, each thoughtfully organized to lead students from fundamental principles to advanced complexities. Beginning with the establishment of Lebesgue?s measure on the real line and an introduction to measurable functions, the book then delves into exploring the cardinalities of various set classes. As readers progress, the subtleties of the Lebesgue integral emerge, showcasing its generalization of the Riemann integral and its unique characteristics in higher dimensions. One of the book?s distinctive aspects is its indepth comparison of the Lebesgue integral, improper Riemann integral, and Newton integral, shedding light on their distinct qualities and relative independence. Subsequent chapters delve into the realm of general measures, Lebesgue-Stieltje's measure, Hausdorff ?s measure, and the concept of measure and integration in product spaces. Furthermore, the book delves into function spaces, such as ???????? spaces, and navigates the intricacies of signed and complex measures, providing students with a comprehensive foundation in this vital area of mathematics. 410 0$aUniversity Texts in the Mathematical Sciences,$x2731-9326 606 $aMeasure theory 606 $aAssociative rings 606 $aAssociative algebras 606 $aFunctions of real variables 606 $aMeasure and Integration 606 $aAssociative Rings and Algebras 606 $aReal Functions 615 0$aMeasure theory. 615 0$aAssociative rings. 615 0$aAssociative algebras. 615 0$aFunctions of real variables. 615 14$aMeasure and Integration. 615 24$aAssociative Rings and Algebras. 615 24$aReal Functions. 676 $a515.42 700 $aMukhopadhyay$b Satya N$0516085 701 $aRay$b Subhasis$01265599 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910983484303321 996 $aMeasure and Integration$94316917 997 $aUNINA