LEADER 04152nam 22004935 450 001 9911016071803321 005 20250723130327.0 010 $a3-031-95369-X 024 7 $a10.1007/978-3-031-95369-9 035 $a(CKB)39698089800041 035 $a(MiAaPQ)EBC32228478 035 $a(Au-PeEL)EBL32228478 035 $a(DE-He213)978-3-031-95369-9 035 $a(EXLCZ)9939698089800041 100 $a20250723d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLectures on Real-valued Functions /$fby Alexander Kharazishvili 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (697 pages) 311 08$a3-031-95368-1 327 $aChapter 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. 330 $aThis 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 with fairly traditional themes of real analysis and classical measure theory, more profound questions are thoroughly discussed in the book ? appropriate extensions and restrictions of functions, oscillation functions and their characterization, discontinuous functions on resolvable topological spaces, pointwise limits of finite sums of periodic functions, some general results on invariant and quasi-invariant measures, the structure of non-measurable sets and functions, the Baire property of functions on topological spaces and its connections with measurability properties of functions, logical and set-theoretical aspects of the behavior of real-valued functions. . 606 $aMathematics 606 $aFunctions of real variables 606 $aMathematics 606 $aReal Functions 615 0$aMathematics. 615 0$aFunctions of real variables. 615 14$aMathematics. 615 24$aReal Functions. 676 $a510 700 $aKharazishvili$b Alexander$01258282 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911016071803321 996 $aLectures on Real-Valued Functions$94409941 997 $aUNINA