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Real Analysis by Dr. Maria Cristina Pereyra
This text is evolved from authors lecture notes on the subject, and thus is very much oriented towards a pedagogical perspective; much of the key material is contained inside exercises, and in many cases author chosen to give a lengthy and tedious, but instructive, proof instead of a slick abstract proof. Topics covered includes: The natural numbers, Set theory, Integers and rationals, The real numbers, Limits of sequences, Series, Infinite sets, Continuous functions on R, Differentiation of functions, The Riemann integral, the decimal system and basics of mathematical logic.
Author(s): Dr. Maria Cristina Pereyra
171 Pages 
Lecture Notes on Real Analysis by Xiaojing Ye
This note covers preliminaries, Measure and measurable sets, Measurable functions, Lebesgue integral, Signed measures and differentiations, Lp spaces and probability theory.
Author(s): Xiaojing Ye
76 Pages
Lecture Notes on Real Analysis by Nicolas Lerner
This note covers the following topics: Basic structures of topology and metrics, Basic tools of Functional Analysis, Theory of Distributions, Fourier Analysis, Analysis on Hilbert spaces.
Author(s): Nicolas Lerner
170 Pages
Introduction to Real Analysis by Liviu I. Nicolaescu
This note covers the following topics: mathematical reasoning, The Real Number System, Special classes of real numbers, Limits of sequences, Limits of functions, Continuity, Differential calculus, Applications of differential calculus, Integral calculus, Complex numbers and some of their applications, The geometry and topology of Euclidean spaces, Continuity, Multi-variable differential calculus, Applications of multi-variable differential calculus, Multidimensional Riemann integration, Integration over submanifolds.
Author(s): Liviu I. Nicolaescu
696 Pages
This note is an activity-oriented companion to the study of real analysis. It is intended as a pedagogical companion for the beginner, an introduction to some of the main ideas in real analysis, a compendium of problems, are useful in learning the subject, and an annotated reading or reference list. Topics covered includes: Sets, Functions, Cardinality, Groups, Vector Spaces, And Algebras, Partially Ordered Sets, The Real Numbers, Sequences And Indexed Families, Categories, Ordered Vector Spaces, Topological Spaces, Continuity And Weak Topologies, Normed Linear Spaces, Differentiation, Complete Metric Spaces, Algebras And Lattices Of Continuous Functions.
Author(s): John M. Erdman
265 Pages