From Classical to Modern Analysis

• Main Author: Schinazi, Rinaldo B. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Edition: 1st ed. 2018.
• Subjects: Functional analysis.; Functions of real variables.; Measure theory.; Functional Analysis.; Real Functions.; Measure and Integration.

This innovative textbook bridges the gap between undergraduate analysis and graduate measure theory by guiding students from the classical foundations of analysis to more modern topics like metric spaces and Lebesgue integration. Designed for a two-semester introduction to real analysis, the text gi...

Table of Contents:

• 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.