Probability and measure:
Gespeichert in:
1. Verfasser: | |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
New York [u.a.]
Wiley
1995
|
Ausgabe: | 3. ed. |
Schriftenreihe: | Wiley series in probability and mathematical statistics
|
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XII, 593 S. graph. Darst. |
ISBN: | 9780471007104 0471804789 0471007102 |
Internformat
MARC
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100 | 1 | |a Billingsley, Patrick |d 1925-2011 |e Verfasser |0 (DE-588)171977858 |4 aut | |
245 | 1 | 0 | |a Probability and measure |c Patrick Billingsley |
250 | |a 3. ed. | ||
264 | 1 | |a New York [u.a.] |b Wiley |c 1995 | |
300 | |a XII, 593 S. |b graph. Darst. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 0 | |a Wiley series in probability and mathematical statistics | |
650 | 7 | |a Meettechniek |2 gtt | |
650 | 4 | |a Mesure, Théorie de la | |
650 | 7 | |a Mesure, théorie de la |2 ram | |
650 | 4 | |a Probabilités | |
650 | 7 | |a Probabilités |2 ram | |
650 | 7 | |a Waarschijnlijkheidstheorie |2 gtt | |
650 | 4 | |a Measure theory | |
650 | 4 | |a Probabilities | |
650 | 0 | 7 | |a Wahrscheinlichkeitstheorie |0 (DE-588)4079013-7 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Wahrscheinlichkeitsrechnung |0 (DE-588)4064324-4 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
_version_ | 1804124738263449600 |
---|---|
adam_text | Contents
CHAPTER
1.
PROBABILITY
1.
Borel s Normal Number Theorem,
1
The Unit Interval
—
The Weak Law of Large Numbers
—
The Strong
Law of Large Numbers
—
Strong Law Versus Weak
—
Length
—
The Measure Theory of Diophantine Approximation*
2.
Probability Measures,
17
Spaces
—
Assigning Probabilities
—
Classes of Sets
—
Probability
Measures
—
Lebesgue Measure on the Unit Interval
—
Sequence
Space*
—
Constructing
σ
-Fields*
3.
Existence and Extension,
36
Construction of the Extension
—
Uniqueness and the
π-λ
Theorem
—
Monotone Classes
—
Lebesgue Measure on the Unit Interval
—
Completeness
—
Nonmeasurable Sets
—
Two Impossibility Theorems*
4.
Denumerable Probabilities,
51
General Formulas
—
Limit Sets
—
Independent Events
—
Subfields
—
The Borel-Cantelli Lemmas
—
The Zero-One Law
5.
Simple Random Variables,
67
Definition
—
Convergence of Random Variables
—
Independence
—
Existence of Independent Sequences
—
Expected Value
—
Inequalities
6.
The Law of Large Numbers,
85
The Strong Law
—
The Weak Law
—
Bernstein s Theorem
—
A Refinement of the Second Borel-Cantelli Lemma
Stars indicate topics that may be omitted on a first reading.
vii
VIU
CONTENTS
7.
Gambling Systems,
92
Gambler s Ruin
—
Selection Systems
—
Gambling Policies
—
Bold Play*—Timid Play*
8.
Markov Chains,
111
Definitions
—
Higher-Order Transitions
—
An Existence Theorem
—
Transience and Persistence
—
Another Criterion for Persistence
—
Stationary Distributions
—
Exponential Convergence*
—
Optimal
Stopping
*
9.
Large Deviations and the Law of the Iterated Logarithm,*
145
Moment Generating Functions
—
Large Deviations
—
Chernoff s
Theorem
—
The Law of the Iterated Logarithm
CHAPTER
2.
MEASURE
158
10.
General Measures,
158
Classes of Sets
—
Conventions Involving
<»—
Measures
—
Uniqueness
11.
Outer Measure,
165
Outer Measure
—
Extension
—
An Approximation Theorem
12.
Measures in Euclidean Space,
171
Lebesgue Measure
—
Regularity
—
Specifying Measures on the
Line
—
Specifying Measures in Rk
—
Strange Euclidean Sets*
13.
Measurable Functions and Mappings,
182
Measurable Mappings
—
Mappings into Rk
—
Limits
and Measureability
—
Transformations of Measures
14.
Distribution Functions,
187
Distribution Functions
—
Exponential Distributions
—
Weak
Convergence
—
Convergence of Types*
—
Extremal Distributions*
CHAPTER
3.
INTEGRATION
199
15.
The Integral,
199
Definition
—
Nonnegative
Functions
—
Uniqueness
CONTENTS 1X
16.
Properties of the Integral,
206
Equalities and Inequalities
—
Integration to the Limit
—
Integration
over Sets
—
Densities
—
Change of Variable
—
Uniform Integrability
—
Complex Functions
17.
The Integral with Respect to Lebesgue Measure,
221
The Lebesgue Integral on the Line
—
The Riemann Integral
—
The Fundamental Theorem of Calculus
—
Change of Variable
—
The Lebesgue Integral in Rk
—
Stieltjes
Integrals
18.
Product Measure and Fubini s Theorem,
231
Product Spaces
—
Product Measure
—
Fubini s Theorem
—
Integration by Parts
—
Products of Higher Order
19.
The L Spaces,*
241
Definitions
—
Completeness and Separability
—
Conjugate Spaces
—
Weak Compactness
—
Some Decision Theory
—
The Space
L2
—
An Estimation Problem
CHAPTER
4.
RANDOM VARIABLES
AND EXPECTED VALUES
254
20.
Random Variables and Distributions,
254
Random Variables and Vectors
—
Subfields
—
Distributions
—
Multidimensional Distributions
—
Independence
—
-Sequences
of Random Variables
—
Convolution
—
Convergence in Probability
—
The Glivenko
-Cantelli
Theorem*
21.
Expected Values,
273
Expected Value as Integral
—
Expected Values and Limits
—
Expected Values and Distributions
—
Moments
—
Inequalities
—
Joint Integrals
—
Independence and Expected Value
—
Moment
Generating Functions
22.
Sums of Independent Random Variables,
282
The Strong Law of Large Numbers
—
The Weak Law and Moment
Generating Functions
—
Kolmogorov s Zero-One Law
—
Maximal
Inequalities
—
Convergence of Random Series
—
Random Taylor
Series
*
CONTENTS
23. The
Poisson
Process,
297
Characterization of the Exponential Distribution
—
The
Poisson
Process
—
The
Poisson
Approximation
—
Other Characterizations
of the
Poisson
Process
—
Stochastic Processes
24.
The Ergodic Theorem,*
310
Measure-Preserving Transformations
—
Ergodicity
—
Ergodicity
of Rotations
—
Proof of the Ergodic Theorem
—
The Continued-
Fraction Transformation
—
Diophantine Approximation
CHAPTER
5.
CONVERGENCE OF DISTRIBUTIONS
327
25.
Weak Convergence,
327
Definitions
—
Uniform Distribution Modulo
1*—
Convergence
in Distribution
—
Convergence in Probability
—
Fundamental
Theorems
—
Helly
s
Theorem
—
Integration to the Limit
26.
Characteristic Functions,
342
Definition
—
Moments and Derivatives
—
Independence—Inversion
and the Uniqueness Theorem
—
The Continuity Theorem
—
Fourier Series*
27.
The Central Limit Theorem,
357
Identically Distributed Summands
—
The
Lindeberg
and Lyapounov Theorems
—
Dependent Variables
28.
Infinitely Divisible Distributions,*
371
Vague Convergence
—
The Possible Limits
—
Characterizing
the Limit
29.
Limit Theorems in Rk,
378
The Basic Theorems
—
Characteristic Functions
—
Normal
Distributions in Rk
—
The Central Limit Theorem
30.
The Method of Moments,*
388
The Moment Problem
—
Moment Generating Functions
—
Central
Limit Theorem by Moments
—
Application to Sampling Theory
—
Application to Number Theory
CONTENTS
Χ»
CHAPTER
6. DERIVATIVES
AND CONDITIONAL
PROBABILITY
400
31.
Derivatives on the Line,*
400
The Fundamental Theorem of Calculus
—
Derivatives of Integrals
—
Singular Functions
—
Integrals of Derivatives
—
Functions
of Bounded Variation
32.
The Radon-Nikodym Theorem,
419
Additive Set Functions
—
The
Hahn
Decomposition
—
Absolute
Continuity and Singularity
—
The Main Theorem
33.
Conditional Probability,
427
The Discrete Case
—
The General Case
—
Properties of Conditional
Probability
—
Difficulties and Curiosities
—
Conditional Probability
Distributions
34.
Conditional Expectation,
445
Definition
—
Properties of Conditional Expectation
—
Conditional
Distributions and Expectations
—
Sufficient Subfields*
—
Minimum-Variance Estimation
*
35.
Martingales,
458
Definition -Submartingdales
—
Gambling
—
Functions
of Martingales
—
Stopping Times
—
Inequalities
—
Convergence
Theorems
—
Applications: Derivatives
—
Likelihood Ratios
—
Reversed Martingales
—
Applications:
de
Finetti s Theorem
—
Bayes
Estimation
—
A Central Limit Theorem*
CHAPTER
7.
STOCHASTIC PROCESSES
482
36.
Kolmogorov s Existence Theorem,
482
Stochastic Processes
—
Finite-Dimensional Distributions
—
Product
Spaces
—
Kolmogorov s Existence Theorem
—
The Inadequacy
of
â$T
—
A Return to Ergodic Theory*
—
The Hewitt-Savage
Theorem
*
37.
Brownian Motion,
498
Definition
—
Continuity of Paths
—
Measurable Processes
—
Irregularity of Brownian Motion Paths
—
The Strong Markov
Property
—
The Reflection Principle
—
Skorohod Embedding*
—
Invariance
*
Xli
CONTENTS
38.
Nondenumerable
Probabilities,*
526
Introduction
—
Definitions
—
Existence
Theorems—Consequences
of Separability
APPENDIX 536
NOTES ON THE PROBLEMS 552
BIBLIOGRAPHY 581
LIST OF SYMBOLS 585
INDEX 587
|
any_adam_object | 1 |
author | Billingsley, Patrick 1925-2011 |
author_GND | (DE-588)171977858 |
author_facet | Billingsley, Patrick 1925-2011 |
author_role | aut |
author_sort | Billingsley, Patrick 1925-2011 |
author_variant | p b pb |
building | Verbundindex |
bvnumber | BV010318695 |
callnumber-first | Q - Science |
callnumber-label | QA273 |
callnumber-raw | QA273 |
callnumber-search | QA273 |
callnumber-sort | QA 3273 |
callnumber-subject | QA - Mathematics |
classification_rvk | QH 170 SK 430 SK 800 |
classification_tum | MAT 600f MAT 280f |
ctrlnum | (OCoLC)246792596 (DE-599)BVBBV010318695 |
dewey-full | 519.2 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 519 - Probabilities and applied mathematics |
dewey-raw | 519.2 |
dewey-search | 519.2 |
dewey-sort | 3519.2 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik Wirtschaftswissenschaften |
edition | 3. ed. |
format | Book |
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id | DE-604.BV010318695 |
illustrated | Illustrated |
indexdate | 2024-07-09T17:50:26Z |
institution | BVB |
isbn | 9780471007104 0471804789 0471007102 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006866471 |
oclc_num | 246792596 |
open_access_boolean | |
owner | DE-384 DE-739 DE-824 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-20 DE-703 DE-29T DE-634 DE-83 DE-188 |
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physical | XII, 593 S. graph. Darst. |
publishDate | 1995 |
publishDateSearch | 1995 |
publishDateSort | 1995 |
publisher | Wiley |
record_format | marc |
series2 | Wiley series in probability and mathematical statistics |
spelling | Billingsley, Patrick 1925-2011 Verfasser (DE-588)171977858 aut Probability and measure Patrick Billingsley 3. ed. New York [u.a.] Wiley 1995 XII, 593 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics Meettechniek gtt Mesure, Théorie de la Mesure, théorie de la ram Probabilités Probabilités ram Waarschijnlijkheidstheorie gtt Measure theory Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Maßtheorie (DE-588)4074626-4 s DE-188 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s 1\p DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006866471&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Billingsley, Patrick 1925-2011 Probability and measure Meettechniek gtt Mesure, Théorie de la Mesure, théorie de la ram Probabilités Probabilités ram Waarschijnlijkheidstheorie gtt Measure theory Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Maßtheorie (DE-588)4074626-4 gnd |
subject_GND | (DE-588)4079013-7 (DE-588)4064324-4 (DE-588)4074626-4 |
title | Probability and measure |
title_auth | Probability and measure |
title_exact_search | Probability and measure |
title_full | Probability and measure Patrick Billingsley |
title_fullStr | Probability and measure Patrick Billingsley |
title_full_unstemmed | Probability and measure Patrick Billingsley |
title_short | Probability and measure |
title_sort | probability and measure |
topic | Meettechniek gtt Mesure, Théorie de la Mesure, théorie de la ram Probabilités Probabilités ram Waarschijnlijkheidstheorie gtt Measure theory Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Maßtheorie (DE-588)4074626-4 gnd |
topic_facet | Meettechniek Mesure, Théorie de la Mesure, théorie de la Probabilités Waarschijnlijkheidstheorie Measure theory Probabilities Wahrscheinlichkeitstheorie Wahrscheinlichkeitsrechnung Maßtheorie |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006866471&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT billingsleypatrick probabilityandmeasure |