Coverart for item
The Resource The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence : A Primer, by John Toland, (electronic resource)

The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence : A Primer, by John Toland, (electronic resource)

Label
The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence : A Primer
Title
The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence
Title remainder
A Primer
Statement of responsibility
by John Toland
Creator
Subject
Language
eng
Summary
In measure theory, a familiar representation theorem due to F. Riesz identifies the dual space Lp(X,L,λ)* with Lq(X,L,λ), where 1/p+1/q=1, as long as 1 ≤ p<∞. However, L∞(X,L,λ)* cannot be similarly described, and is instead represented as a class of finitely additive measures. This book provides a reasonably elementary account of the representation theory of L∞(X,L,λ)*, examining pathologies and paradoxes, and uncovering some surprising consequences. For instance, a necessary and sufficient condition for a bounded sequence in L∞(X,L,λ) to be weakly convergent, applicable in the one-point compactification of X, is given. With a clear summary of prerequisites, and illustrated by examples including L∞(Rn) and the sequence space l∞, this book makes possibly unfamiliar material, some of which may be new, accessible to students and researchers in the mathematical sciences.--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Toland, John
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
Series statement
  • SpringerBriefs in Mathematics,
  • Springer eBooks.
http://library.link/vocab/subjectName
  • Measure theory
  • Functional analysis
  • Calculus of variations
  • Sequences (Mathematics)
Label
The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence : A Primer, by John Toland, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-030-34732-1
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1 Introduction -- 2 Notation and Preliminaries -- 3 L∞ and its Dual -- 4 Finitely Additive Measures -- 5 G: 0-1 Finitely Additive Measures -- 6 Integration and Finitely Additive Measures -- 7 Topology on G -- 8 Weak Convergence in L∞(X,L,λ) -- 9 L∞* when X is a Topological Space -- 10 Reconciling Representations -- References -- Index
Control code
978-3-030-34732-1
Dimensions
unknown
Edition
1st ed. 2020.
Extent
1 online resource (X, 99 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783030347321
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
1 illustration
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1140955989
Label
The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence : A Primer, by John Toland, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-030-34732-1
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1 Introduction -- 2 Notation and Preliminaries -- 3 L∞ and its Dual -- 4 Finitely Additive Measures -- 5 G: 0-1 Finitely Additive Measures -- 6 Integration and Finitely Additive Measures -- 7 Topology on G -- 8 Weak Convergence in L∞(X,L,λ) -- 9 L∞* when X is a Topological Space -- 10 Reconciling Representations -- References -- Index
Control code
978-3-030-34732-1
Dimensions
unknown
Edition
1st ed. 2020.
Extent
1 online resource (X, 99 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783030347321
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
1 illustration
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1140955989

Library Locations

    • Badia FiesolanaBorrow it
      Via dei Roccettini 9, San Domenico di Fiesole, 50014, IT
      43.803074 11.283055
Processing Feedback ...