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020 _a9781461469568
_99781461469568
024 7 _a10.1007/9781461469568
_2doi
035 _avtls000342059
039 9 _a201509030328
_bVLOAD
_c201405050238
_dVLOAD
_y201402061116
_zstaff
040 _aMX-SnUAN
_bspa
_cMX-SnUAN
_erda
050 4 _aQA312-312.5
100 1 _aCohn, Donald L.
_eautor
_9321137
245 1 0 _aMeasure Theory :
_bSecond Edition /
_cby Donald L. Cohn.
250 _a2nd ed. 2013.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Birkhäuser,
_c2013.
300 _axxI, 457 páginas 7 ilustraciones
_brecurso en línea.
336 _atexto
_btxt
_2rdacontent
337 _acomputadora
_bc
_2rdamedia
338 _arecurso en línea
_bcr
_2rdacarrier
347 _aarchivo de texto
_bPDF
_2rda
490 0 _aBirkhäuser Advanced Texts Basler Lehrbücher,
_x1019-6242
500 _aSpringer eBooks
505 0 _a1. Measures -- Algebras and sigma-algebras -- Measures -- Outer measures -- Lebesgue measure -- Completeness and regularity -- Dynkin classes -- 2. Functions and Integrals -- Measurable functions -- Properties that hold almost everywhere -- The integral -- Limit theorems -- The Riemann integral -- Measurable functions again, complex-valued functions, and image measures -- 3. Convergence -- Modes of Convergence -- Normed spaces -- Definition of L^p and L^p -- Properties of L^p and L-p -- Dual spaces -- 4. Signed and Complex Measures -- Signed and complex measures -- Absolute continuity -- Singularity -- Functions of bounded variation -- The duals of the L^p spaces -- 5. Product Measures -- Constructions -- Fubini’s theorem -- Applications -- 6. Differentiation -- Change of variable in R^d -- Differentiation of measures -- Differentiation of functions -- 7. Measures on Locally Compact Spaces -- Locally compact spaces -- The Riesz representation theorem -- Signed and complex measures; duality -- Additional properties of regular measures -- The µ^*-measurable sets and the dual of L^1 -- Products of locally compact spaces -- 8. Polish Spaces and Analytic Sets -- Polish spaces -- Analytic sets -- The separation theorem and its consequences -- The measurability of analytic sets -- Cross sections -- Standard, analytic, Lusin, and Souslin spaces -- 9. Haar Measure -- Topological groups -- The existence and uniqueness of Haar measure -- The algebras L^1 (G) and M (G) -- Appendices -- A. Notation and set theory -- B. Algebra -- C. Calculus and topology in R^d -- D. Topological spaces and metric spaces -- E. The Bochner integral -- F Liftings -- G The Banach-Tarski paradox -- H The Henstock-Kurzweil and McShane integralsBibliography -- Index of notation -- Index.
520 _aIntended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and the existence of liftings. Measure Theory provides a solid background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review of essential background material.   The author aims to present  a straightforward treatment of the part of measure theory necessary for analysis and probability' assuming only basic knowledge of analysis and topology...Each chapter includes numerous well-chosen exercises, varying from very routine practice problems to important extensions and developments of the theory; for the difficult ones there are helpful hints. It is the reviewer's opinion that the author has succeeded in his aim. In spite of its lack of new results, the selection and presentation of materials makes this a useful book for an introduction to measure and integration theory. —Mathematical Reviews (Review of the First Edition)   The book is a comprehensive and clearly written textbook on measure and integration...The book contains appendices on set theory, algebra, calculus and topology in Euclidean spaces, topological and metric spaces, and the Bochner integral. Each section of the book contains a number of exercises.   —zbMATH (Review of the First Edition)
590 _aPara consulta fuera de la UANL se requiere clave de acceso remoto.
710 2 _aSpringerLink (Servicio en línea)
_9299170
776 0 8 _iEdición impresa:
_z9781461469551
856 4 0 _uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-1-4614-6956-8
_zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
942 _c14
999 _c290418
_d290418