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Lecture Notes for Integration
Aim of this lecture note is to develop an understanding of the statements of the theorems and how to apply them carefully. Major topics covered are: Measure spaces, Outer measure, null set, measurable set, The Cantor set, Lebesgue measure on the real line, Counting measure, Probability measures, Construction of a non-measurable set , Measurable function, simple function, integrable function, Reconciliation with the integral introduced in Prelims, Simple comparison theorem, Theorems of Fubini and Tonelli.
Author(s): Z. Qian and Alison Etheridge
NA Pages 
Integral Calculus Miguel A. Lerma
The contents of this book include: Integrals, Applications of Integration, Differential Equations, Infinite Sequences and Series, Hyperbolic Functions, Various Formulas, Table of Integrals.
Author(s): Miguel A. Lerma
120 Pages
This graduate-level lecture note covers Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transform.
Author(s): Prof. Jeff Viaclovsky
NA Pages
The Integration of Functions of a Single Variable
This book describes the following topics: Elementary functions and their classification, The integration of elementary functions, The integration of rational functions, The integration of algebraical functions and The integration of transcendental functions.
Author(s): G. H. Hardy
NA Pages
This lecture note explains the following topics: The integral: properties and construction, Function spaces, Probability, Random walk and martingales, Radon integrals.
Author(s): William G. Faris
72 Pages