Limits a New Approach to Real Analysis

A unique approach to analysis that lets you apply mathematics across a range of subjects
This innovative text sets forth a thoroughly rigorous modern account of the theoretical underpinnings of calculus: continuity, differentiability, and convergence. Using a constructive approach, every proof of every result is direct and ultimately computationally verifiable. In particular, existence is never established by showing that the assumption of non-existence leads to a contradiction. The ultimate consequence of this method is that it makes sensenot just to math majors but also to students from all branches of the sciences.

Authors: Loeb, Peter A
Written by one of the leading scholars in the field Includes a novel presentation of differentiation and absolute continuity using a local maximum function, resulting in an exposition that is both simpler and more general than the traditional approach
Theorems are stated for Lebesgue and Borel measures, with a note indicating when the same proof works only for Lebesgue measures
Appendices cover additional material, including theorems for higher dimensions and a short introduction to nonstandard analysis