Lectures on Real-valued Functions

Chapter 1. Unary and Binary Relations.- Chapter 2. Partial Functions and Functions.- Chapter 3. Elementary Facts on Cardinal Numbers.- Chapter 4. Some Properties of the Continuum.- Chapter 5. The Oscillation of a Real-valued Function at a Point.- Chapter 6. Points of Continuity and Discontinuity of Real-valued Functions.- Chapter 7. Real-valued Monotone Functions.- Chapter 8. Real-valued Convex Functions.- Chapter 9. Semicontinuity of a Real-valued Function at a Point.- Chapter 10. Semicontinuous Real-valued Functions on Quasi-compact Spaces.- Chapter 11. The Banach–Steinhaus Theorem.- Chapter 12. A Characterization of Oscillation Functions.- Chapter 13. Semicontinuity versus Continuity.- Chapter 14. The Outer Measures.- Chapter 15. Finitely Additive and Countably Additive Measures.- Chapter 16. Extensions of Measures.- Chapter 17. Caratheodory’s and Marczewski’s Extension Theorems.- Chapter 18. Positive Linear Functionals.- Chapter 19. The Nonexistence of Universal Countably Additive Measures.- Chapter 20. Radon Measures.- Chapter 21. Invariant and Quasi-invariant Measures.- Chapter 22. Pointwise Limits of Finite Sums of Periodic Functions.- Chapter 23. Absolutely Nonmeasurable Setsin Commutative Groups.- Chapter 24. Radon Spaces.- Chapter 25. Nonmeasurable Sets with respect to Radon Measures.- Chapter 26. The Radon–Nikodym Theorem.- Chapter 27. Decompositions of Linear Functionals.- Chapter 28. Linear Continuous Functionals and Radon Measures.- Chapter 29. Linear Continuous Functionalson a Real Hilbert Space.- Chapter 30. Baire Property in Topological Spaces.- Chapter 31. The Stone–Weierstrass Theorem.- Chapter 32. More on the Function Space C(X).- Chapter 33. Uniformization of Plane Sets by Relatively Measurable Functions.

• Erscheinungsdatum: 22.07.2025
• Autor/Autorin: Alexander Kharazishvili
• Reihe: Mathematics and Statistics (R0)
• Format: E-Book
• Dateiformat: PDF
• Kopierschutz: Wasserzeichen
• Dateigröße: 9.2 MB
• Verlag: SPRINGER
• Sprache: Englisch
• Umfang: 452 Seiten
• ISBN: 9783031953699
• Lieferung: Sofort per Download
• Hinweis: Sofort per Download lieferbar. Kein physischer Versand.
• Kompatibilität: Lesbar auf Geräten und Apps mit PDF-Unterstützung.