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 Irena Swanson - Reed College
Students learn to write proofs while at the same time learning about binary operations, orders, fields, ordered fields, complete fields, complex numbers, sequences, and series. We also review limits, continuity, differentiation, and integration.
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 J. Ponstein
This book is concerned with an attempt to introduce the infinitesimals and the other 'nonstandard' numbers in a naive, simpleminded way. Nevertheless, the resulting theory is hoped to be mathematically sound, and to be complete within obvious limits.
by Francisco Bulnes - InTech
The purpose is to present a complete course on global analysis topics and establish some orbital applications of the integration on topological groups and their algebras to harmonic analysis and induced representations in representation theory.