Lectures on Functional Analysis and the Lebesgue Integral
This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension. This approach leads naturally to the basic notions and th...
| Κύριος συγγραφέας: | |
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| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
London :
Springer London : Imprint: Springer,
2016.
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| Σειρά: | Universitext,
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| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- Some papers of general interest
- Topological prerequisites
- Part 1 Functional analysis
- Hilbert spaces
- Banach spaces
- Locally convex spaces
- Part 2 The Lebesgue integral
- Monotone functions.- The Lebesgue integral in R
- Generalized Newton-Leibniz formula
- Integrals on measure spaces
- Part 3 Function spaces.- Spaces of continuous functions
- Spaces of integrable functions
- Almost everywhere convergence
- Hints and solutions to some exercises.- Bibliography
- Teaching remarks
- Subject index
- Name index.
