**by Sheldon Axler**

DescriptionDetailsHashtagsReport an issue ### Book Description

This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics.Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn.Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder's Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability.Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. ### Book Details

### Related Books

This open book is licensed under a Creative Commons License (CC BY-NC). You can download Measure, Integration & Real Analysis ebook for free in PDF format (6.2 MB).

Title

Measure, Integration & Real Analysis

Subject

Science and Mathematics

Publisher

Springer

Published

2020

Pages

430

Edition

1

Language

English

ISBN13

9783030331429

ISBN10

3030331423

ISBN13 Digital

9783030331436

ISBN10 Digital

3030331431

PDF Size

6.2 MB

License

This easy-to-follow textbook/reference presents a concise introduction to mathematical analysis from an algorithmic point of view, with a particular focus on applications of analysis and aspects of mathematical modelling. The text describes the mathematical theory alongside the basic concepts and methods of numerical analysis, enriched by computer ...

If you understand basic mathematics and know how to program with Python, you're ready to dive into signal processing. While most resources start with theory to teach this complex subject, this practical book introduces techniques by showing you how they're applied in the real world. In the first chapter alone, you'll be able to decom...

This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overvie...

Much of the data available today is unstructured and text-heavy, making it challenging for analysts to apply their usual data wrangling and visualization tools. With this practical book, you'll explore text-mining techniques with tidytext, a package that authors Julia Silge and David Robinson developed using the tidy principles behind R packag...

This open book is a dynamic guide incorporating the essential skills needed to build a foundation in Financial Analysis. Students and readers will learn how to insightfully read a Financial Statement, utilize key financial ratios in order to derive forward-looking investment-related inferences from the accounting data, engage in elementary forecast...

This book presents a comparative analysis of intergroup relations and migrant integration at the neighbourhood level in Europe. Featuring a unique collection of portraits of urban relations between the majority population and immigrant minorities, it examines how relations are structured and evolve in different and increasingly diverse local societ...