Integration with Respect to Finitely Additive Measures View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1991

AUTHORS

Wilhelmus A. J. Luxemburg

ABSTRACT

This essay interprets the theory of finitely additive measures within the framework of the theory of Riesz spaces. The following topics are discussed: the extension procedures of measures, the Riemann and the Dunford integration procedures, the Radon-Nikodym Theorem and the Hahn Decomposition Theorem, the representation theory of the Radon- Nikodym derivatives as generalized functions, conditional expectation operators, the theory of Lp-spaces, and the norm completeness problem.The nature of the classical axiom of countable additivity is examined from Carathéodory’s algebraic measure-theoretic point of view. More... »

PAGES

109-150

Book

TITLE

Positive Operators, Riesz Spaces, and Economics

ISBN

978-3-642-63502-1
978-3-642-58199-1

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-58199-1_6

DOI

http://dx.doi.org/10.1007/978-3-642-58199-1_6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1037142243


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Mathematics, Caltech, 91125, Pasadena, CA, USA", 
          "id": "http://www.grid.ac/institutes/grid.20861.3d", 
          "name": [
            "Department of Mathematics, Caltech, 91125, Pasadena, CA, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Luxemburg", 
        "givenName": "Wilhelmus A. J.", 
        "id": "sg:person.016621530177.98", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016621530177.98"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "1991", 
    "datePublishedReg": "1991-01-01", 
    "description": "This essay interprets the theory of finitely additive measures within the framework of the theory of Riesz spaces. The following topics are discussed: the extension procedures of measures, the Riemann and the Dunford integration procedures, the Radon-Nikodym Theorem and the Hahn Decomposition Theorem, the representation theory of the Radon- Nikodym derivatives as generalized functions, conditional expectation operators, the theory of Lp-spaces, and the norm completeness problem.The nature of the classical axiom of countable additivity is examined from Carath\u00e9odory\u2019s algebraic measure-theoretic point of view.", 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-642-58199-1_6", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-642-63502-1", 
        "978-3-642-58199-1"
      ], 
      "name": "Positive Operators, Riesz Spaces, and Economics", 
      "type": "Book"
    }, 
    "keywords": [
      "measure-theoretic point", 
      "additive measures", 
      "Radon-Nikodym derivative", 
      "Radon-Nikodym theorem", 
      "Hahn decomposition theorem", 
      "Lp-spaces", 
      "conditional expectation operator", 
      "representation theory", 
      "expectation operator", 
      "countable additivity", 
      "decomposition theorem", 
      "Riesz spaces", 
      "integration procedure", 
      "completeness problem", 
      "extension procedure", 
      "theorem", 
      "classical axioms", 
      "theory", 
      "Riemann", 
      "operators", 
      "axioms", 
      "space", 
      "problem", 
      "following topics", 
      "framework", 
      "procedure", 
      "derivatives", 
      "function", 
      "point", 
      "additivity", 
      "measures", 
      "integration", 
      "respect", 
      "topic", 
      "nature", 
      "view", 
      "essay", 
      "Dunford integration procedures", 
      "norm completeness problem", 
      "Carath\u00e9odory\u2019s algebraic measure-theoretic point", 
      "\u2019s algebraic measure-theoretic point"
    ], 
    "name": "Integration with Respect to Finitely Additive Measures", 
    "pagination": "109-150", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1037142243"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-642-58199-1_6"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-642-58199-1_6", 
      "https://app.dimensions.ai/details/publication/pub.1037142243"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2021-12-01T20:12", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20211201/entities/gbq_results/chapter/chapter_66.jsonl", 
    "type": "Chapter", 
    "url": "https://doi.org/10.1007/978-3-642-58199-1_6"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-58199-1_6'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-58199-1_6'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-58199-1_6'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-58199-1_6'


 

This table displays all metadata directly associated to this object as RDF triples.

95 TRIPLES      22 PREDICATES      66 URIs      59 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-642-58199-1_6 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N99fab887b3c74cbdb810517f6cad05e8
4 schema:datePublished 1991
5 schema:datePublishedReg 1991-01-01
6 schema:description This essay interprets the theory of finitely additive measures within the framework of the theory of Riesz spaces. The following topics are discussed: the extension procedures of measures, the Riemann and the Dunford integration procedures, the Radon-Nikodym Theorem and the Hahn Decomposition Theorem, the representation theory of the Radon- Nikodym derivatives as generalized functions, conditional expectation operators, the theory of Lp-spaces, and the norm completeness problem.The nature of the classical axiom of countable additivity is examined from Carathéodory’s algebraic measure-theoretic point of view.
7 schema:genre chapter
8 schema:inLanguage en
9 schema:isAccessibleForFree false
10 schema:isPartOf N2e2a7994100b43cd914746c0b79ed761
11 schema:keywords Carathéodory’s algebraic measure-theoretic point
12 Dunford integration procedures
13 Hahn decomposition theorem
14 Lp-spaces
15 Radon-Nikodym derivative
16 Radon-Nikodym theorem
17 Riemann
18 Riesz spaces
19 additive measures
20 additivity
21 axioms
22 classical axioms
23 completeness problem
24 conditional expectation operator
25 countable additivity
26 decomposition theorem
27 derivatives
28 essay
29 expectation operator
30 extension procedure
31 following topics
32 framework
33 function
34 integration
35 integration procedure
36 measure-theoretic point
37 measures
38 nature
39 norm completeness problem
40 operators
41 point
42 problem
43 procedure
44 representation theory
45 respect
46 space
47 theorem
48 theory
49 topic
50 view
51 ’s algebraic measure-theoretic point
52 schema:name Integration with Respect to Finitely Additive Measures
53 schema:pagination 109-150
54 schema:productId N1bbab6da9e6c439fbca2f588a198c144
55 N6479704af5ed4656a275a70a087b13ab
56 schema:publisher N451f517a53074adfb7f81519a8b17246
57 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037142243
58 https://doi.org/10.1007/978-3-642-58199-1_6
59 schema:sdDatePublished 2021-12-01T20:12
60 schema:sdLicense https://scigraph.springernature.com/explorer/license/
61 schema:sdPublisher Ndbf8222ce54b437480b24126327c0413
62 schema:url https://doi.org/10.1007/978-3-642-58199-1_6
63 sgo:license sg:explorer/license/
64 sgo:sdDataset chapters
65 rdf:type schema:Chapter
66 N1bbab6da9e6c439fbca2f588a198c144 schema:name dimensions_id
67 schema:value pub.1037142243
68 rdf:type schema:PropertyValue
69 N2e2a7994100b43cd914746c0b79ed761 schema:isbn 978-3-642-58199-1
70 978-3-642-63502-1
71 schema:name Positive Operators, Riesz Spaces, and Economics
72 rdf:type schema:Book
73 N451f517a53074adfb7f81519a8b17246 schema:name Springer Nature
74 rdf:type schema:Organisation
75 N6479704af5ed4656a275a70a087b13ab schema:name doi
76 schema:value 10.1007/978-3-642-58199-1_6
77 rdf:type schema:PropertyValue
78 N99fab887b3c74cbdb810517f6cad05e8 rdf:first sg:person.016621530177.98
79 rdf:rest rdf:nil
80 Ndbf8222ce54b437480b24126327c0413 schema:name Springer Nature - SN SciGraph project
81 rdf:type schema:Organization
82 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
83 schema:name Mathematical Sciences
84 rdf:type schema:DefinedTerm
85 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
86 schema:name Pure Mathematics
87 rdf:type schema:DefinedTerm
88 sg:person.016621530177.98 schema:affiliation grid-institutes:grid.20861.3d
89 schema:familyName Luxemburg
90 schema:givenName Wilhelmus A. J.
91 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016621530177.98
92 rdf:type schema:Person
93 grid-institutes:grid.20861.3d schema:alternateName Department of Mathematics, Caltech, 91125, Pasadena, CA, USA
94 schema:name Department of Mathematics, Caltech, 91125, Pasadena, CA, USA
95 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...