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Lectures on Real-valued Functions

This book offers several topics of mathematical analysis which are closely connected with significant properties of real-valued functions of various types (such as semi-continuous functions, monotone functions, convex functions, measurable functions, additive and linear functionals, etc.). Alongside...

Täydet tiedot

Tallennettuna:
Bibliografiset tiedot
Päätekijä: Kharazishvili, Alexander (Tekijä)
Yhteisötekijä: SpringerLink (Online service)
Aineistotyyppi: Elektroninen E-kirja
Kieli:englanti
Julkaistu: Cham : Springer Nature Switzerland : Imprint: Springer, 2025.
Painos:1st ed. 2025.
Aiheet:
Mathematics.
Functions of real variables.
Real Functions.
Linkit:https://doi.org/10.1007/978-3-031-95369-9
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Sisällysluettelo:
  • 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.

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