.

0 (hodnocen0 x )

BK

1st ed.

Praha : Matfyzpress, 1995

178 s. ; 30 cm

ISBN 80-85863-06-5 (brož.)

Název z obálky

Vydavatel: Matematicko-fyzikální fakulta University Karlovy

Obsahuje bibliografii na s. 162-170 a rejstřík

000239095

Contents // List of Basic Notations and Frequently Used Symbols...1 // A. Measures and Measurable Functions...2 // 1. The Lebesgue Measure // 2. Abstract Measures // 3. Measurable Functions // 4. Construction of Measures from Outer Measures // 5. Classes of Sets and Set Functions // 6. Signed and Complex Measures // B. The Abstract Lebesgue Integral...21 // 7. Integration on R // 8. The Abstract Lebesgue Integral // 9. Integrals Depending on a Parameter // 10. The LP Spaces // 11. Product Measures and the Fubini Theorem // 12. Sequences of Measurable Functions // 13. The Radon-Nikodym Theorem and the Lebesgue Decomposition // C. Radon Integral and Measure...45 // 14. Radon Integral and Radon Outer Measure // 15. Radon Measures // 16. Riesz Representation Theorem // 17. Sequences of Measures // 18. Luzin’s Theorem // 19. Measures on Topological Groups // D. Integration on R...65 // 20. Integral and Differentiation // 21. Functions of Finite Variation and Absolutely Continuous Functions // 22. Theorems on Almost Everywhere Differentiation // 23. Indefinite Lebesgue Integral and Absolute Continuity // 24. Radon Measures on R and Distribution Functions // 25. Henstock-Kurzweil Integral // E. Integration on Rn...81 // 26. Lebesgue Measure and Integral on R" // 27. Covering Theorems // 28. Differentiation of Measures // 29. Lebesgue Density Theorem and Approximately Continuous Functions // 30. Lipschitz Functions // 31. Approximation Theorems // 32. Distributions // 33. Fourier Transform

// F. Change of Variable Formula and k-dimensional Measures...111 // 34. Change of Variable Theorem // 35. The Degree of a Mapping // 36. Hausdorff Measures // G. Surface and Curve Integrals...129 // 37. Integral Calculus in Vector Analysis // 38. Integration of Differential Forms // 39. Integration on Manifolds // H. Vector Integration...151 // 40. Measurable Functions // 41. Vector Measures // 42. The Bochner Integral // 43. The Dunford and Pettis Integrals // Appendix on Topology...160 // References...162 // A Short Guide to the Notation...171 // Subject Index...173