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Integration Theory Lecture notes
This note introduces the concepts of measures, measurable functions and Lebesgue integrals. Topics covered includes: Measurable functions / random variables , Dynkin’s Lemma and the Uniqueness Theorem, Borel-Cantelli’s First Lemma, Independent random variables, Kolmogorov’s 0-1-law, Integration of nonnegative functions , Jordan-Hahn Decompositions, The Lebesgue-Radon-Nikodym Theorem, The law of large numbers.
Author(s): Johan Jonasson
71 Pages 
This note covers the following topics: Elementary Integrals, Substitution, Trigonometric integrals, Integration by parts, Trigonometric substitutions, Partial Fractions.
Author(s): Mark MacLean and Andrew Rechnitzer
96 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
Integration Theory Lecture notes
This note introduces the concepts of measures, measurable functions and Lebesgue integrals. Topics covered includes: Measurable functions / random variables , Dynkin’s Lemma and the Uniqueness Theorem, Borel-Cantelli’s First Lemma, Independent random variables, Kolmogorov’s 0-1-law, Integration of nonnegative functions , Jordan-Hahn Decompositions, The Lebesgue-Radon-Nikodym Theorem, The law of large numbers.
Author(s): Johan Jonasson
71 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