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An illustrative introduction to modern analysis

By: Katzourakis, Nikos.
Contributor(s): Varvaruca, Eugen [Co author].
Material type: materialTypeLabelBookPublisher: New York CRC Press 2018Edition: 1st.Description: xv, 541p. With index.ISBN: 9781138718272.Subject(s): Mathematical analysisAdditional physical formats: No titleDDC classification: 515 Online resources: View item Summary: Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis.The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required. https://www.crcpress.com/An-Illustrative-Introduction-to-Modern-Analysis/Katzourakis-Varvaruca/p/book/9781138718272
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Table of Contents
1 Sets, mappings, countability and choice
2 Metric spaces and normed spaces
3 Completeness and applications
4 Topological spaces and continuity
5 Compactness and sequential compactness
6 The Lebesgue measure on the Euclidean space
7 Measure theory on general spaces
8 The Lebesgue integration theory
9 The class of Lebesgue functional spaces
10 Inner product spaces and Hilbert spaces
11 Linear operators on normed spaces
12 Weak topologies on Banach spaces
13 Weak* topologies and compactness
14 Functional properties of the Lebesgue spaces
15 Solutions to the exercises

Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis.The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required.

https://www.crcpress.com/An-Illustrative-Introduction-to-Modern-Analysis/Katzourakis-Varvaruca/p/book/9781138718272

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