Reader-friendly Introduction to the Measure Theory
by Vasily Nekrasov
Publisher: Yetanotherquant.de 2009
Number of pages: 117
This is a very clear and user-friendly introduction to the Lebesgue measure theory. The fundamental ideas of the Lebesgue measure are discussed comprehensively, so after reading these notes, you will be able to read any book on Real Analysis and will easily understand Lebesgue integral and other advanced topics.
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by E. E. Rosinger - arXiv
These notes offer a short and rigorous introduction to Nostandard Analysis, mainly aimed to reach to a presentation of the basics of Loeb integration, and in particular, Loeb measures. The Abraham Robinson version of Nostandard Analysis is pursued.
by Sean Mauch - Caltech
Advanced mathematical methods for scientists and engineers, it contains material on calculus, functions of a complex variable, ordinary differential equations, partial differential equations and the calculus of variations.
by L. Schwartz - Tata Institute of Fundamental Research
These Notes cover I) disintegration of a measure with respect to a single sigma-algebra, and in part II, measure valued supermartingales and regular disintegration of a measure with respect to an increasing right continuous family of sigma-algebras.
by Eckhard Hitzer - arXiv
This paper treats the fundamentals of the multivector differential calculus part of geometric calculus. The multivector differential is introduced, followed by the multivector derivative and the adjoint of multivector functions.