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From Classical to Modern Analysis
ISBN-13:
9783319945835
Veröffentl:
2018
Seiten:
270
Autor:
Rinaldo B. Schinazi
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
To build the foundational elements of real analysis, the first seven chapters cover number systems, convergence of sequences and series, as well as more advanced topics like superior and inferior limits, convergence of functions, and metric spaces. Chapters 8 through 12 explore topology in and continuity on metric spaces and introduce the Lebesgue integrals. The last chapters are largely independent and discuss various applications of the Lebesgue integral.
Preface.- Real Numbers.- Sequences of Real Numbers.- Limits Superior and Inferior of a Sequence.- Numerical Series.- Convergence of Functions.- Power Series.- Metric Spaces.- Topology in a Metric Space.- Continuity on Metric Spaces.- Measurable Sets and Measurable Functions.- Measures.- The Lebesgue Integral.- Integrals with Respect to Counting Measures.- Riemann and Lebesgue Integrals.- Modes of Convergance.- References.
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