Measures, integrals and martingales:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2005
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Klappentext Inhaltsverzeichnis |
| Physical Description: | X, 381 S. graph. Darst. |
| ISBN: | 0521850150 9780521850155 0521615259 9780521615259 |
Staff View
MARC
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| 245 | 1 | 0 | |a Measures, integrals and martingales |c René L. Schilling |
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| 650 | 4 | |a Martingales (Mathematics) | |
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Record in the Search Index
| _version_ | 1804133773234667520 |
|---|---|
| adam_text | Measures, integrals and Martingales
This is
integration theory as needed nowadays in many parts of analysis
and probability theory. The basictheory: measures, integrals,
convergence theorems, Lp-spaces and multiple integrals, is
explored in the first part of the book. The second part then uses
the notion of martingales to develop the theory further, covering
topics such asjacobi s General Transformation Theorem, the
Radon-Nikodým
Hardy-Littlewood maximal functions or general Fourier series.
Undergraduate calculus and an introductory course on rigorous
analysis in
text suitable for both lecture courses and for self-study.
Numerous illustrations and exercises are included and these are
not merely drill problems but are there to consolidate what has
already been learnt and to discover variants, asides and
extensions to the main material. Hints and solutions will be
available on the internet.
Contents
Pielitele
Dependence chart
1
Problems
2
Problems
3
Problems
4
Problems
5
Problems
6
Problems
7
Problems
8
Problems
9
Problems
10
Null sets and the a.e.
Problems
vi
11
Parameter-dependent integrals
Riemann vs. Lebesgue integration
Examples
Problems
12
Problems
13
More on measurable functions
Distribution functions
Minkowski s inequality for integrals
Problems
14
Convolutions
Problems
15
Jacobi s transformation formula
Spherical coordinates and the volume of the unit ball
Continuous functions are dense in Lp( )
Regular measures
Problems
16
Different forms of uniform integrability
Problems
17
Problems
18
Problems
19
of martingales
The
Martingale inequalities
The Hardy-Littlewood maximal theorem
Lebesgue
The
Problems
Contents
20
Problems
21
Problems
22
On the structure of subspaces of L2
Problems
23
Classical conditional expectations
Separability criteria for the spaces LP(X,
Problems
24
Orthogonal polynomials
The trigonometric system and Fourier series
The
The
The Rademacher functions
Well-behaved
Problems
Appendix
Appendix B: Some facts from point-set topology
Topological spaces
Metric spaces
Normed spaces
Appendix C: The volume of a parallelepiped
Appendix D: Non-measurable sets
Appendix
The (proper) Riemann integral
The fundamental theorem of integral calculus
Integrals and limits
Improper Riemann integrals
Further reading
References
Notation index
Name and subject index
|
| any_adam_object | 1 |
| author | Schilling, René L. 1969- |
| author_GND | (DE-588)122050045 |
| author_facet | Schilling, René L. 1969- |
| author_role | aut |
| author_sort | Schilling, René L. 1969- |
| author_variant | r l s rl rls |
| building | Verbundindex |
| bvnumber | BV020820275 |
| callnumber-first | Q - Science |
| callnumber-label | QA312 |
| callnumber-raw | QA312 QC20.7.M43 |
| callnumber-search | QA312 QC20.7.M43 |
| callnumber-sort | QA 3312 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 150 SK 430 |
| ctrlnum | (OCoLC)60611040 (OCoLC)255158994 (DE-599)BVBBV020820275 |
| dewey-full | 515.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.42 |
| dewey-search | 515.42 |
| dewey-sort | 3515.42 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. publ. |
| format | Book |
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| genre_facet | Einführung |
| id | DE-604.BV020820275 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:14:02Z |
| institution | BVB |
| isbn | 0521850150 9780521850155 0521615259 9780521615259 |
| language | English |
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| physical | X, 381 S. graph. Darst. |
| publishDate | 2005 |
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| publisher | Cambridge Univ. Press |
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| spelling | Schilling, René L. 1969- Verfasser (DE-588)122050045 aut Measures, integrals and martingales René L. Schilling 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2005 X, 381 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Intégrales Martingales (Mathématiques) Mesure, Théorie de la Integrals Martingales (Mathematics) Measure theory Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Maßtheorie (DE-588)4074626-4 s Integrationstheorie (DE-588)4138369-2 s 1\p DE-604 DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013525655&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013525655&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Schilling, René L. 1969- Measures, integrals and martingales Intégrales Martingales (Mathématiques) Mesure, Théorie de la Integrals Martingales (Mathematics) Measure theory Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4138369-2 (DE-588)4074626-4 (DE-588)4151278-9 |
| title | Measures, integrals and martingales |
| title_auth | Measures, integrals and martingales |
| title_exact_search | Measures, integrals and martingales |
| title_full | Measures, integrals and martingales René L. Schilling |
| title_fullStr | Measures, integrals and martingales René L. Schilling |
| title_full_unstemmed | Measures, integrals and martingales René L. Schilling |
| title_short | Measures, integrals and martingales |
| title_sort | measures integrals and martingales |
| topic | Intégrales Martingales (Mathématiques) Mesure, Théorie de la Integrals Martingales (Mathematics) Measure theory Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Intégrales Martingales (Mathématiques) Mesure, Théorie de la Integrals Martingales (Mathematics) Measure theory Integrationstheorie Maßtheorie Einführung |
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