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Real Analysis Study Material
The subject of real analysis is concerned with studying the behavior and properties of functions, sequences, and sets on the real number line, which we denote as the mathematically familiar R. This note explains the following topics: Continuous Functions on Intervals, Bolzano’s Intermediate Value Theorem, Uniform Continuity, The Riemann Integrals, Fundamental Theorems Of Calculus, Pointwise and Uniform Convergence, Uniform Convergence and Continuity, Series Of Functions, Improper Integrals of First Kind, Beta and Gamma Functions.
Author(s): Nandakumar, University of Calicut
145 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
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
Spaces An Introduction to Real Analysis
This note explains the following topics: Preliminaries: Proofs, Sets, and Functions, The Foundation of Calculus, Metric Spaces, Spaces of Continuous Functions, Modes of continuity, Applications to differential equations, Applications to power series.
Author(s): Tom L. Lindstrom
148 Pages