Shortcuts
Top of page (Alt+0)
Page content (Alt+9)
Page menu (Alt+8)
Your browser does not support javascript, some WebOpac functionallity will not be available.
.
Default
.
PageMenu
-
Main Menu
-
Simple Search
.
Advanced Search
.
Journal Search
.
Refine Search Results
.
Preferences
.
Search Menu
Simple Search
.
Advanced Search
.
New Items Search
.
Journal Search
.
Refine Search Results
.
Bottom Menu
Help
Italian
.
English
.
German
.
New Item Menu
New Items Search
.
New Items List
.
Links
SISSA Library
.
ICTP library
.
Italian National web catalog (SBN)
.
Trieste University web catalog
.
Udine University web catalog
.
© LIBERO v6.4.1sp220816
Page content
You are here
:
Catalogue Display
Catalogue Display
Classical Potential Theory and Its Probabilistic Counterpart
.
Bookmark this Record
Catalogue Record 42758
.
.
Author info on Wikipedia
.
.
LibraryThing
.
.
Google Books
.
.
Amazon Books
.
Catalogue Information
Catalogue Record 42758
.
Reviews
Catalogue Record 42758
.
British Library
Resolver for RSN-42758
Google Scholar
Resolver for RSN-42758
WorldCat
Resolver for RSN-42758
Catalogo Nazionale SBN
Resolver for RSN-42758
GoogleBooks
Resolver for RSN-42758
ICTP Library
Resolver for RSN-42758
.
Share Link
Jump to link
Catalogue Information
Field name
Details
Dewey Class
515.96
Title
Classical Potential Theory and Its Probabilistic Counterpart ([EBook]) / by Joseph L. Doob.
Author
Doob, Joseph L. , 1910-2004
Other name(s)
SpringerLink (Online service)
Publication
Berlin, Heidelberg : Springer , 2001.
Physical Details
L, 1551 pages : online resource.
Series
Classics in mathematics
1431-0821
ISBN
9783642565731
Summary Note
From the reviews: "This huge book written in several years by one of the few mathematicians able to do it, appears as a precise and impressive study (not very easy to read) of this bothsided question that replaces, in a coherent way, without being encyclopaedic, a large library of books and papers scattered without a uniform language. Instead of summarizing the author gives his own way of exposition with original complements. This requires no preliminary knowledge. ...The purpose which the author explains in his introduction, i.e. a deep probabilistic interpretation of potential theory and a link between two great theories, appears fulfilled in a masterly manner". M. Brelot in Metrika (1986).:
Contents note
I Introduction to the Mathematical Background of Classical Potential Theory -- II Basic Properties of Harmonic, Subharmonic, and Superharmonic Functions -- III Infima of Families of Superharmonic Functions -- IV Potentials on Special Open Sets -- V Polar Sets and Their Applications -- VI The Fundamental Convergence Theorem and the Reduction Operation -- VII Green Functions -- VIII The Dirichlet Problem for Relative Harmonic Functions -- IX Lattices and Related Classes of Functions -- X The Sweeping Operation -- XI The Fine Topology -- XII The Martin Boundary -- XIII Classical Energy and Capacity -- XIV One-Dimensional Potential Theory -- XV Parabolic Potential Theory: Basic Facts -- XVI Subparabolic, Superparabolic, and Parabolic Functions on a Slab -- XVII Parabolic Potential Theory (Continued) -- XVIII The Parabolic Dirichlet Problem, Sweeping, and Exceptional Sets -- XIX The Martin Boundary in the Parabolic Context -- I Fundamental Concepts of Probability -- II Optional Times and Associated Concepts -- III Elements of Martingale Theory -- IV Basic Properties of Continuous Parameter Supermartingales -- V Lattices and Related Classes of Stochastic Processes -- VI Markov Processes -- VII Brownian Motion -- VIII The Itô Integral -- IX Brownian Motion and Martingale Theory -- X Conditional Brownian Motion -- I Lattices in Classical Potential Theory and Martingale Theory -- II Brownian Motion and the PWB Method -- III Brownian Motion on the Martin Space -- Appendixes -- Appendix I -- Analytic Sets -- 1. Pavings and Algebras of Sets -- 2. Suslin Schemes -- 3. Sets Analytic over a Product Paving -- 4. Analytic Extensions versus ? Algebra Extensions of Pavings -- 7. Projections of Sets in Product Pavings -- 8. Extension of a Measurability Concept to the Analytic Operation Context -- 10. Polish Spaces -- 11. The Baire Null Space -- 12. Analytic Sets -- 13. Analytic Subsets of Polish Spaces -- Appendix II -- Capacity Theory -- 1. Choquet Capacities -- 2. Sierpinski Lemma -- 3. Choquet Capacity Theorem -- 4. Lusin’s Theorem -- 5. A Fundamental Example of a Choquet Capacity -- 6. Strongly Subadditive Set Functions -- 7. Generation of a Choquet Capacity by a Positive Strongly Subadditive Set Function -- 8. Topological Precapacities -- 9. Universally Measurable Sets -- Appendix III -- Lattice Theory -- 1. Introduction -- 2. Lattice Definitions -- 3. Cones -- 4. The Specific Order Generated by a Cone -- 5. Vector Lattices -- 6. Decomposition Property of a Vector Lattice -- 7. Orthogonality in a Vector Lattice -- 8. Bands in a Vector Lattice -- 9. Projections on Bands -- 10. The Orthogonal Complement of a Set -- 11. The Band Generated by a Single Element -- 12. Order Convergence -- 13. Order Convergence on a Linearly Ordered Set -- Appendix IV -- Lattice Theoretic Concepts in Measure Theory -- 1. Lattices of Set Algebras -- 2. Measurable Spaces and Measurable Functions -- 3. Composition of Functions -- 4. The Measure Lattice of a Measurable Space -- 5. The ? Finite Measure Lattice of a Measurable Space (Notation of Section 4) -- 6. The Hahn and Jordan Decompositions -- 8. Absolute Continuity and Singularity -- 9. Lattices of Measurable Functions on a Measure Space -- 10.Order Convergence of Families of Measurable Functions -- 11. Measures on Polish Spaces -- 12. Derivates of Measures -- Appendix V -- Uniform Integrability -- Appendix VI -- Kernels and Transition Functions -- 1. Kernels -- 2. Universally Measurable Extension of a Kernel -- 3. Transition Functions -- Appendix VII -- Integral Limit Theorems -- 1. An Elementary Limit Theorem -- 2. Ratio Integral Limit Theorems -- 3. A One-Dimensional Ratio Integral Limit Theorem -- 4. A Ratio Integral Limit Theorem Involving Convex Variational Derivates -- Appendix VIII -- Lower Semicontinuous Functions -- 1. The Lower Semicontinuous Smoothing of a Function -- 2. Suprema of Families of Lower Semicontinuous Functions -- 3. Choquet Topological Lemma -- Historical Notes -- 1 -- 2 -- 3 -- Appendixes -- Notation Index.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-3-642-56573-1
Links to Related Works
Subject References:
Mathematics
.
Potential Theory
.
Potential theory (Mathematics)
.
Probabilities
.
Probability theory and stochastic processes
.
Authors:
Doob, Joseph L. 1910-2004
.
Doob, Joseph L., 1910-2004
.
Corporate Authors:
SpringerLink (Online service)
.
Series:
Classics in mathematics
.
Classification:
515.96
.
.
ISBD Display
Catalogue Record 42758
.
Tag Display
Catalogue Record 42758
.
Related Works
Catalogue Record 42758
.
Marc XML
Catalogue Record 42758
.
Add Title to Basket
Catalogue Record 42758
.
Catalogue Information 42758
Beginning of record
.
Catalogue Information 42758
Top of page
.
Download Title
Catalogue Record 42758
Export
This Record
As
Labelled Format
Bibliographic Format
ISBD Format
MARC Format
MARC Binary Format
MARCXML Format
User-Defined Format:
Title
Author
Series
Publication Details
Subject
To
File
Email
Reviews
This item has not been rated.
Add a Review and/or Rating
42758
1
42758
-
2
42758
-
3
42758
-
4
42758
-
5
42758
-
Quick Search
Search for