Independent random variables and rearrangement invariant spaces /:
The subject of this book lies on the boundary between probability theory and the theory of function spaces. Here Professor Braverman investigates independent random variables in rearrangement invariant (r.i.) spaces. The significant feature of r.i. spaces is that the norm of an element depends on it...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1994.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
194. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The subject of this book lies on the boundary between probability theory and the theory of function spaces. Here Professor Braverman investigates independent random variables in rearrangement invariant (r.i.) spaces. The significant feature of r.i. spaces is that the norm of an element depends on its distribution only, and this property allows the results and methods associated with r.i. spaces to be applied to problems in probability theory. On the other hand, probabilistic methods can also prove useful in the study of r.i. spaces. In this book new techniques are used and a number of interesting results are given. Most of the results are due to the author but have never before been available in English. Here they are all presented together in a volume that will be essential reading for all serious researchers in this area. |
| Beschreibung: | 1 online resource (viii, 115 pages) |
| Bibliographie: | Includes bibliographical references (pages 113-115) and index. |
| ISBN: | 9781107362017 1107362016 9780511662348 0511662343 |
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| 245 | 1 | 0 | |a Independent random variables and rearrangement invariant spaces / |c Michael Sh. Braverman. |
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| 505 | 0 | |a Ch. I. Preliminaries. 1. Rearrangement invariant spaces. 2. The function of dilatation and Boyd indices. 3. Independent random variables. 4. Probability inequalities. 5. Disjoint random variables. 6. The Kruglov property. 7. Bases and sequence spaces. 8. Stable distributions -- Ch. II. Inequalities for sums of independent random variables in rearrangement invariant spaces. 1. Rosenthal's inequality and a characterization of the spaces L[subscript p]. 2. Estimates of von Bahr-Esseen type. 3. Upper estimates of the Rosenthal type. 4. Estimates in exponential Orlicz spaces -- Ch. III. Linear combinations of independent random variables in rearrangement invariant spaces. 1. l[subscript q]-estimates [actual symbol not reproducible]. 2. l[subscript 2]-estimates. 3. Stable random variables with different exponents. 4. Equidistributed random variables in exponential Orlicz spaces -- Ch. IV. Complementability of subspaces generated by independent random variables. | |
| 588 | 0 | |a Print version record. | |
| 520 | |a The subject of this book lies on the boundary between probability theory and the theory of function spaces. Here Professor Braverman investigates independent random variables in rearrangement invariant (r.i.) spaces. The significant feature of r.i. spaces is that the norm of an element depends on its distribution only, and this property allows the results and methods associated with r.i. spaces to be applied to problems in probability theory. On the other hand, probabilistic methods can also prove useful in the study of r.i. spaces. In this book new techniques are used and a number of interesting results are given. Most of the results are due to the author but have never before been available in English. Here they are all presented together in a volume that will be essential reading for all serious researchers in this area. | ||
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| contents | Ch. I. Preliminaries. 1. Rearrangement invariant spaces. 2. The function of dilatation and Boyd indices. 3. Independent random variables. 4. Probability inequalities. 5. Disjoint random variables. 6. The Kruglov property. 7. Bases and sequence spaces. 8. Stable distributions -- Ch. II. Inequalities for sums of independent random variables in rearrangement invariant spaces. 1. Rosenthal's inequality and a characterization of the spaces L[subscript p]. 2. Estimates of von Bahr-Esseen type. 3. Upper estimates of the Rosenthal type. 4. Estimates in exponential Orlicz spaces -- Ch. III. Linear combinations of independent random variables in rearrangement invariant spaces. 1. l[subscript q]-estimates [actual symbol not reproducible]. 2. l[subscript 2]-estimates. 3. Stable random variables with different exponents. 4. Equidistributed random variables in exponential Orlicz spaces -- Ch. IV. Complementability of subspaces generated by independent random variables. |
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| indexdate | 2024-11-27T13:25:17Z |
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| series2 | London Mathematical Society lecture note series ; |
| spelling | Braverman, Michael Sh. Independent random variables and rearrangement invariant spaces / Michael Sh. Braverman. Cambridge ; New York : Cambridge University Press, 1994. 1 online resource (viii, 115 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 194 Includes bibliographical references (pages 113-115) and index. Ch. I. Preliminaries. 1. Rearrangement invariant spaces. 2. The function of dilatation and Boyd indices. 3. Independent random variables. 4. Probability inequalities. 5. Disjoint random variables. 6. The Kruglov property. 7. Bases and sequence spaces. 8. Stable distributions -- Ch. II. Inequalities for sums of independent random variables in rearrangement invariant spaces. 1. Rosenthal's inequality and a characterization of the spaces L[subscript p]. 2. Estimates of von Bahr-Esseen type. 3. Upper estimates of the Rosenthal type. 4. Estimates in exponential Orlicz spaces -- Ch. III. Linear combinations of independent random variables in rearrangement invariant spaces. 1. l[subscript q]-estimates [actual symbol not reproducible]. 2. l[subscript 2]-estimates. 3. Stable random variables with different exponents. 4. Equidistributed random variables in exponential Orlicz spaces -- Ch. IV. Complementability of subspaces generated by independent random variables. Print version record. The subject of this book lies on the boundary between probability theory and the theory of function spaces. Here Professor Braverman investigates independent random variables in rearrangement invariant (r.i.) spaces. The significant feature of r.i. spaces is that the norm of an element depends on its distribution only, and this property allows the results and methods associated with r.i. spaces to be applied to problems in probability theory. On the other hand, probabilistic methods can also prove useful in the study of r.i. spaces. In this book new techniques are used and a number of interesting results are given. Most of the results are due to the author but have never before been available in English. Here they are all presented together in a volume that will be essential reading for all serious researchers in this area. Random variables. http://id.loc.gov/authorities/subjects/sh85111355 Rearrangement invariant spaces. http://id.loc.gov/authorities/subjects/sh96011300 Inequalities (Mathematics) http://id.loc.gov/authorities/subjects/sh85065985 Variables aléatoires. Inégalités (Mathématiques) MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Inequalities (Mathematics) fast Random variables fast Rearrangement invariant spaces fast Topologischer Vektorraum gnd http://d-nb.info/gnd/4122383-4 Unabhängige Zufallsvariable gnd http://d-nb.info/gnd/4205983-5 Waarschijnlijkheidstheorie. gtt Functieruimten. gtt Processos estocasticos. larpcal Variables aléatoires. ram Sous espaces invariants. ram Inégalités (Mathématiques) ram has work: Independet random variables and rearrangement invariant spaces (Text) https://id.oclc.org/worldcat/entity/E39PCY6Tbm3bw6GvVDkwRwdG73 https://id.oclc.org/worldcat/ontology/hasWork Print version: Braverman, Michael Sh. Independent random variables and rearrangement invariant spaces. Cambridge ; New York : Cambridge University Press, 1994 0521455154 (DLC) 96105776 (OCoLC)31415502 London Mathematical Society lecture note series ; 194. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552467 Volltext |
| spellingShingle | Braverman, Michael Sh Independent random variables and rearrangement invariant spaces / London Mathematical Society lecture note series ; Ch. I. Preliminaries. 1. Rearrangement invariant spaces. 2. The function of dilatation and Boyd indices. 3. Independent random variables. 4. Probability inequalities. 5. Disjoint random variables. 6. The Kruglov property. 7. Bases and sequence spaces. 8. Stable distributions -- Ch. II. Inequalities for sums of independent random variables in rearrangement invariant spaces. 1. Rosenthal's inequality and a characterization of the spaces L[subscript p]. 2. Estimates of von Bahr-Esseen type. 3. Upper estimates of the Rosenthal type. 4. Estimates in exponential Orlicz spaces -- Ch. III. Linear combinations of independent random variables in rearrangement invariant spaces. 1. l[subscript q]-estimates [actual symbol not reproducible]. 2. l[subscript 2]-estimates. 3. Stable random variables with different exponents. 4. Equidistributed random variables in exponential Orlicz spaces -- Ch. IV. Complementability of subspaces generated by independent random variables. Random variables. http://id.loc.gov/authorities/subjects/sh85111355 Rearrangement invariant spaces. http://id.loc.gov/authorities/subjects/sh96011300 Inequalities (Mathematics) http://id.loc.gov/authorities/subjects/sh85065985 Variables aléatoires. Inégalités (Mathématiques) MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Inequalities (Mathematics) fast Random variables fast Rearrangement invariant spaces fast Topologischer Vektorraum gnd http://d-nb.info/gnd/4122383-4 Unabhängige Zufallsvariable gnd http://d-nb.info/gnd/4205983-5 Waarschijnlijkheidstheorie. gtt Functieruimten. gtt Processos estocasticos. larpcal Variables aléatoires. ram Sous espaces invariants. ram Inégalités (Mathématiques) ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85111355 http://id.loc.gov/authorities/subjects/sh96011300 http://id.loc.gov/authorities/subjects/sh85065985 http://d-nb.info/gnd/4122383-4 http://d-nb.info/gnd/4205983-5 |
| title | Independent random variables and rearrangement invariant spaces / |
| title_auth | Independent random variables and rearrangement invariant spaces / |
| title_exact_search | Independent random variables and rearrangement invariant spaces / |
| title_full | Independent random variables and rearrangement invariant spaces / Michael Sh. Braverman. |
| title_fullStr | Independent random variables and rearrangement invariant spaces / Michael Sh. Braverman. |
| title_full_unstemmed | Independent random variables and rearrangement invariant spaces / Michael Sh. Braverman. |
| title_short | Independent random variables and rearrangement invariant spaces / |
| title_sort | independent random variables and rearrangement invariant spaces |
| topic | Random variables. http://id.loc.gov/authorities/subjects/sh85111355 Rearrangement invariant spaces. http://id.loc.gov/authorities/subjects/sh96011300 Inequalities (Mathematics) http://id.loc.gov/authorities/subjects/sh85065985 Variables aléatoires. Inégalités (Mathématiques) MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Inequalities (Mathematics) fast Random variables fast Rearrangement invariant spaces fast Topologischer Vektorraum gnd http://d-nb.info/gnd/4122383-4 Unabhängige Zufallsvariable gnd http://d-nb.info/gnd/4205983-5 Waarschijnlijkheidstheorie. gtt Functieruimten. gtt Processos estocasticos. larpcal Variables aléatoires. ram Sous espaces invariants. ram Inégalités (Mathématiques) ram |
| topic_facet | Random variables. Rearrangement invariant spaces. Inequalities (Mathematics) Variables aléatoires. Inégalités (Mathématiques) MATHEMATICS Applied. MATHEMATICS Probability & Statistics General. Random variables Rearrangement invariant spaces Topologischer Vektorraum Unabhängige Zufallsvariable Waarschijnlijkheidstheorie. Functieruimten. Processos estocasticos. Sous espaces invariants. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552467 |
| work_keys_str_mv | AT bravermanmichaelsh independentrandomvariablesandrearrangementinvariantspaces |