Alexander Kharazishvili
Alexander Kharazishvili is a chief researcher at the A. Razmadze Mathematical Institute of Tbilisi State University and a member of the Georgian National Academy of Sciences. His research interests mainly concern real analysis and measure theory, mostly with various properties of real-valued functions such as topological, algebraic, measure-theoretical, etc. He has more than 300 scientific publications and is the author of the book "Strange Functions in Real Analysis", published by CRC Press. The third edition of this book was published in 2018.
Erschienen am 22.07.2025Lectures on Real-valued Functions
E-Book
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....
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