Homeomorphisms in analysis / / Casper Goffman, Togo Nishiura, Daniel Waterman

• Autore: Goffman Casper <1913->
• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , [1997]; ©1997
• Descrizione fisica: 1 online resource (235 p.)
• Disciplina: 515/.13
• Soggetto topico: Homeomorphisms; Mathematical analysis
• Persona (resp. second.): NishiuraTogo <1931->; WatermanDaniel
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (pages207 -211) and index.
• Nota di contenuto: ""Contents""; ""Preface""; ""The one dimensional case""; ""Mappings and measures on R[sup(n)]""; ""Fourier series""; ""Part 1. The One Dimensional Case""; ""Chapter 1. Subsets of R""; ""1.1. Equivalence classes""; ""1.2. Lebesgue equivalence of sets""; ""1.3. Density topology""; ""1.4. The Zahorski classes""; ""Chapter 2. Baire Class 1""; ""2.1. Characterization""; ""2.2. Absolutely measurable functions""; ""2.3. Example""; ""Chapter 3. Differentiability Classes""; ""3.1. Continuous functions of bounded variation""; ""3.2. Continuously differentiable functions"" ; ""3.3. The class C[sup(n)][0,1]""""3.4. Remarks""; ""Chapter 4. The Derivative Function""; ""4.1. Properties of derivatives""; ""4.2. Characterization of the derivative""; ""4.3. Proof of Maximoff's theorem""; ""4.4. Approximate derivatives""; ""4.5. Remarks""; ""Part 2. Mappings and Measures on R[sup(n)]""; ""Chapter 5. Bi-Lipschitzian Homeomorphisms""; ""5.1. Lebesgue measurability""; ""5.2. Length of nonparametric curves""; ""5.3. Nonparametric area""; ""5.4. Invariance under self-homeomorphisms""; ""5.5. Invariance of approximately continuous functions""; ""5.6. Remarks"" ; ""Chapter 6. Approximation by Homeomorphisms""""6.1. Background""; ""6.2. Approximations by homeomorphisms of one-to-one maps""; ""6.3. Extensions of homeomorphisms""; ""6.4. Measurable one-to-one maps""; ""Chapter 7. Measures on R[sup(n)]""; ""7.1. Preliminaries""; ""7.2. The one variable case""; ""7.3. Constructions of deformations""; ""7.4. Deformation theorem""; ""7.5. Remarks""; ""Chapter 8. Blumberg's Theorem""; ""8.1. Blumberg's theorem for metric spaces""; ""8.2. Non-Blumberg Baire spaces""; ""8.3. Homeomorphism analogues""; ""Part 3. Fourier Series"" ; ""Chapter 9. Improving the Behavior of Fourier Series""""9.1. Preliminaries""; ""9.2. Uniform convergence""; ""9.3. Conjugate functions and the Pál-Bohr theorem""; ""9.4. Absolute convergence""; ""Chapter 10. Preservation of Convergence of Fourier Series""; ""10.1. Tests for pointwise and uniform convergence""; ""10.2. Fourier series of regulated functions""; ""10.3. Uniform convergence of Fourier series""; ""Chapter 11. Fourier Series of Integrable Functions""; ""11.1. Absolutely measurable functions""; ""11.2. Convergence of Fourier series after change of variable"" ; ""11.3. Functions of generalized bounded variation""""11.4. Preservation of the order of magnitude of Fourier coefficients""; ""Appendix A. Supplementary Material""; ""Sets, Functions and Measures""; ""A.1. Baire, Borel and Lebesgue""; ""A.2. Lipschitzian functions""; ""A.3. Bounded variation""; ""Approximate Continuity""; ""A.4. Density topology""; ""A.5. Approximately continuous maps into metric spaces""; ""Hausdorff Measure and Packing""; ""A.6. Hausdorff dimension""; ""A.7. Hausdorff packing""; ""Nonparametric Length and Area""; ""A.8. Nonparametric length""; ""A.9. Schwarz's example"" ; ""A.10. Lebesgue's lower semicontinuous area""
• Titolo autorizzato: Homeomorphisms in analysis
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910146559703321
• Lo trovi qui: Univ. Federico II
• Serie: Mathematical surveys and monographs ; ; no. 54.