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Book Synopsis

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.

Lectures on Realvalued Functions

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      Publisher: Springer
      Publication Date: Publication Date: 24/08/2025
      ISBN13: 9783031953682, 978-3031953682
      ISBN10:
      Also in:
      Mathematics

      Description

      Book Synopsis

      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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