00000cam a22000004i 4500 UP-1685594773861233100 Buklod 20070906150133.0 m |o d | ta 180202t19971997riu rb |||1 u|eng d 0821806327 1065-7339 (iLib)UPBAG-00000011308 BC-39684 Php2,450.00 DLC BAG rda eng QA 300 L54 1997 Lieb, Elliott H. author. Analysis Elliott H. Lieb, Michael Loss. Providence, Rhode Island American Mathematical Society ©1997. xviii, 278 pages 27 cm Graduate studies in mathematics volume 14 Includes bibliographical references (pages 269-271) and index. Measure and Integration -- Basic notions of measure theory -- Monotone class theorem -- Uniqueness of measures -- Definition of measurable functions and integrals -- Monotone convergence -- Fatou's lemma -- Dominated convergence -- Missing term in Fatou's lemma -- Product measure -- Commutativity and associativity of product measures -- Fubini's theorem -- Layer cake representation -- Bathtub principle -- Constructing a measure from an outer measure -- Uniform convergence except on small sets -- Simple functions and really simple functions -- Approximation by really simple functions -- Approximation by C[superscript infinity] functions -- L[superscript p]-Spaces -- Definition of L[superscript p]-spaces -- Jensen's inequality -- Holder's inequality -- Minkowski's inequality -- Hanner's inequality -- Differentiability of norms -- Completeness of L[superscript p]-spaces -- Projection on convex sets -- Continuous linear functionals and weak convergence -- Linear functionals separate -- Lower semicontinuity of norms -- Uniform boundedness principle -- Strongly convergent convex combinations -- The dual of L[superscript p]([Omega]) -- Convolution -- Approximation by C[superscript infinity]-functions -- Separability of L[superscript p](R[superscript n]) -- Bounded sequences have weak limits -- Approximation by C[superscript infinity subscript c]-functions -- Convolution of functions in dual L[superscript p](R[superscript n])-spaces are continuous -- Hilbert-spaces -- Rearrangement Inequalities. Mathematical analysis. Loss, Michael 1954- author. FO UPBAG UPBAG-MAIN QA 300 L54 1997 Book