LEADER 04069nam 22005415 450 001 9910372749003321 005 20251113174917.0 010 $a3-030-33143-1 024 7 $a10.1007/978-3-030-33143-6 035 $a(CKB)4100000009940077 035 $a(OAPEN)1007045 035 $a(MiAaPQ)EBC6111862 035 $a(DE-He213)978-3-030-33143-6 035 $a(Au-PeEL)EBL6111862 035 $a(OCoLC)1150186447 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/39003 035 $a(PPN)245286780 035 $a(oapen)doab39003 035 $a(EXLCZ)994100000009940077 100 $a20191129d2020 u| 0 101 0 $aeng 135 $auuuuu---auuuu 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMeasure, Integration & Real Analysis /$fby Sheldon Axler 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (411) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v282 311 08$a3-030-33142-3 327 $aAbout the Author -- Preface for Students -- Preface for Instructors -- Acknowledgments -- 1. Riemann Integration -- 2. Measures -- 3. Integration -- 4. Differentiation -- 5. Product Measures -- 6. Banach Spaces -- 7. L^p Spaces -- 8. Hilbert Spaces -- 9. Real and Complex Measures -- 10. Linear Maps on Hilbert Spaces -- 11. Fourier Analysis -- 12. Probability Measures -- Photo Credits -- Bibliography -- Notation Index -- Index -- Colophon: Notes on Typesetting. 330 $aThis open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn?Banach Theorem, Hölder?s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that isfreely available online. 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v282 606 $aMeasure theory 606 $aMeasure and Integration 615 0$aMeasure theory. 615 14$aMeasure and Integration. 676 $a515.42 676 $a515 700 $aAxler$b Sheldon$4aut$4http://id.loc.gov/vocabulary/relators/aut$059614 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910372749003321 996 $aMeasure, Integration & Real Analysis$92169569 997 $aUNINA