From Classical to Modern Analysis

• Κύριος συγγραφέας: Schinazi, Rinaldo B. (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Έκδοση: 1st ed. 2018.
• Θέματα: 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...

Πίνακας περιεχομένων:

• 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.