Publication:
Measure, Integration & Real Analysis

Simple item page
datacite.subject.fos oecd::Natural sciences::Mathematics
dc.contributor.author Sheldon Axler
dc.date.accessioned 2023-06-26T09:05:24Z
dc.date.available 2023-06-26T09:05:24Z
dc.date.issued 2020
dc.description DOI: https://doi.org/10.1007/978-3-030-33143-6 License: CC BY; Publisher: Springer
dc.description.abstract 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.
dc.identifier.doi https://doi.org/10.1007/978-3-030-33143-6
dc.identifier.isbn 9783030331436
dc.identifier.uri http://repository.vlu.edu.vn:443/handle/123456789/5891
dc.language.iso en
dc.subject Measure theory textbook
dc.subject Graduate real analysis textbook
dc.subject Open Access
dc.subject Riemann integration
dc.subject Lebesgue integration
dc.subject Product measures
dc.subject Signed and complex measures
dc.subject Abstract measure
dc.subject Lebesgue Differentiation Theorem
dc.subject Banach spaces
dc.subject Hilbert spaces
dc.subject Hahn–Banach Theorem
dc.subject Hölder’s Inequality
dc.subject Riesz Representation Theorem
dc.subject Spectral Theorem
dc.subject Singular Value Decomposition
dc.subject Fourier analysis
dc.subject Fourier series
dc.subject Fourier transform
dc.subject Open Access math textbook.
dc.title Measure, Integration & Real Analysis
dc.type Resource Types::text::book
dspace.entity.type Publication
oairecerif.author.affiliation #PLACEHOLDER_PARENT_METADATA_VALUE#
Files
Original bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
OAB799.txt
Size:
13 B
Format:
Plain Text
Description:
Download
Collections
Open Access Books - Technology - 2020