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From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further.
The book is intended for the reader who has some experience with proofs, a beginning graduate student for example. It might even be useful to the advanced mathematician who is confronted with situations - such as stochastic integration - where the set-measuring approach to integration does not work.
From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further.
The book is intended for the reader who has some experience with proofs, a beginning graduate student for example. It might even be useful to the advanced mathematician who is confronted with situations - such as stochastic integration - where the set-measuring approach to integration does not work.
Complete and rapid introduction to Lebesgue integration and its generalization
Unusually detailed discussion of Percy Daniell's functional analytic approach to integration
Complemented by interesting historical notes and motivations
Provides numerous exercises and solutions / hints for selected problems
Includes supplementary material: [...]
| Erscheinungsjahr: | 1998 |
|---|---|
| Fachbereich: | Allgemeines |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Thema: | Lexika |
| Medium: | Buch |
| Reihe: | Birkhäuser Advanced Texts Basler Lehrbücher |
| ISBN-13: | 9783764359362 |
| ISBN-10: | 3764359366 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: | Bichteler, Klaus |
| Hersteller: |
Springer Basel
Springer Basel AG Birkhäuser Advanced Texts Basler Lehrbücher |
| Maße: | 241 x 160 x 17 mm |
| Von/Mit: | Klaus Bichteler |
| Erscheinungsdatum: | 19.05.1998 |
| Gewicht: | 0,489 kg |
Complete and rapid introduction to Lebesgue integration and its generalization
Unusually detailed discussion of Percy Daniell's functional analytic approach to integration
Complemented by interesting historical notes and motivations
Provides numerous exercises and solutions / hints for selected problems
Includes supplementary material: [...]
| Erscheinungsjahr: | 1998 |
|---|---|
| Fachbereich: | Allgemeines |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Thema: | Lexika |
| Medium: | Buch |
| Reihe: | Birkhäuser Advanced Texts Basler Lehrbücher |
| ISBN-13: | 9783764359362 |
| ISBN-10: | 3764359366 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: | Bichteler, Klaus |
| Hersteller: |
Springer Basel
Springer Basel AG Birkhäuser Advanced Texts Basler Lehrbücher |
| Maße: | 241 x 160 x 17 mm |
| Von/Mit: | Klaus Bichteler |
| Erscheinungsdatum: | 19.05.1998 |
| Gewicht: | 0,489 kg |
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