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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 contains below topics, Preliminaries, Boolean cumulants of free random variables, Calculus for conditional expectations, Calculus for the block cumulant functional b, Linearization and conditional expectations, Examples, An algebraic approach to Boolean cumulants, Rational series and linearizations.
Author(s): Franz Lehner, Kamil Szpojankowski
58 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
A treatise on the integral calculus with applications examples and problems
This book describes the following topics, Standard Forms, Change Of The Independent Variable,Integration by parts and powers of Sines and cosines, Rational Algebraic Fractional Forms, Reduction Formulae, General Theorems, Differentiation Of a definite Integral with regard to a parameter, Rectification Of Twisted Curves, Moving Curves, Surfaces and volumes in general.
Author(s): Joseph Edwards
946 Pages
Differential and integral calculus
This book consist as a first course in the calculus. In the treatment of each topic, the text is intended to contain a precise statement of the fundamental principle involved, and to insure the students clear understanding of this principle, without districting his attention by the discussion of a multitude of details.
Author(s): Clyde E Love, Earl David Rainville
369 Pages