Real Analysis for Graduate Students: Measure and Integration Theory
by Richard F. Bass
Publisher: CreateSpace 2011
Number of pages: 206
Nearly every Ph.D. student in mathematics needs to take a preliminary or qualifying examination in real analysis. This book provides the necessary tools to pass such an examination. Every effort was made to present the material in as clear a fashion as possible.
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by Lee Larson - University of Louisville
From the table of contents: Basic Ideas (Sets, Functions and Relations, Cardinality); The Real Numbers; Sequences; Series; The Topology of R; Limits of Functions; Differentiation; Integration; Sequences of Functions; Fourier Series.
by John Franks - arXiv
My intent is to introduce the Lebesgue integral in a quick, and hopefully painless, way and then go on to investigate the standard convergence theorems and a brief introduction to the Hilbert space of L2 functions on the interval.
by G. H. Hardy - Cambridge University Press
The ideas of Du Bois-Reymond's 'Infinitarcalcul' are of great and growing importance in all branches of the theory of functions. The author brings the Infinitarcalcul up to date, stating explicitly and proving carefully a number of general theorems.
by B. Lafferriere, G. Lafferriere, N. Mau Nam - Portland State University Library
We provide students with a strong foundation in mathematical analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.