skip to content
Lebesgue integration on Euclidean space Preview this item
ClosePreview this item
Checking...

Lebesgue integration on Euclidean space

Author: Frank Jones
Publisher: Boston : Jones and Bartlett, ©1993.
Series: Jones and Bartlett books in mathematics.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Additional Physical Format: Online version:
Jones, Frank, 1936-
Lebesgue integration on Euclidean space.
Boston : Jones and Bartlett, ©1993
(OCoLC)765609957
Document Type: Book
All Authors / Contributors: Frank Jones
ISBN: 0867202033 9780867202038
OCLC Number: 26211685
Description: xiv, 588 pages : illustrations ; 25 cm.
Contents: 1. Introduction to R[superscript n]. A. Sets. B. Countable Sets. C. Topology. D. Compact Sets. E. Continuity. F. The Distance Function --
2. Lebesgue Measure on R[superscript n]. A. Construction. B. Properties of Lebesgue Measure. C. Appendix: Proof of P1 and P2 --
3. Invariance of Lebesgue Measure. A. Some Linear Algebra. B. Translation and Dilation. C. Orthogonal Matrices. D. The General Matrix --
4. Some Interesting Sets. A.A Nonmeasurable Set. B.A Bevy of Cantor Sets. C. The Lebesgue Function. D. Appendix: The Modulus of Continuity of the Lebesgue Functions --
5. Algebras of Sets and Measurable Functions. A. Algebras and [sigma]-Algebras. B. Borel Sets. C.A Measurable Set which Is Not a Borel Set. D. Measurable Functions. E. Simple Functions --
6. Integration. A. Nonnegative Functions. B. General Measurable Functions. C. Almost Everywhere. D. Integration Over Subsets of R[superscript n]. E. Generalization: Measure Spaces. F. Some Calculations. G. Miscellany --
7. Lebesgue Integral on R[superscript n]. A. Riemann Integral. B. Linear Change of Variables. C. Approximation of Functions in L[superscript 1]. D. Continuity of Translation L[superscript 1] --
8. Fubini's Theorem for R[superscript n]. 9. The Gamma Function. A. Definition and Simple Properties. B. Generalization. C. The Measure of Balls. D. Further Properties of the Gamma Function. E. Stirling's Formula. F. The Gamma Function on R --
10. L[superscript p] Spaces. A. Definition and Basic Inequalities. B. Metric Spaces and Normed Spaces. C. Completeness of L[superscript p]. D. The Case p = [actual symbol not reproducible]. E. Relations between L[superscript p] Spaces. F. Approximation by C[actual symbol not reproducible](R[superscript n]). G. Miscellaneous Problems. H. The Case 0 <p <1 --
11. Products of Abstract Measures. A. Products of [sigma]-Algebras. B. Monotone Classes. C. Construction of the Product Measure. D. The Fubini Theorem. E. The Generalized Minkowski Inequality --
12. Convolutions. A. Formal Properties. B. Basic Inequalities. C. Approximate Identities --
13. Fourier Transform of R[superscript n]. A. Fourier Transform of Functions in L[superscript 1](R[superscript n]). B. The Inversion Theorem. C. The Schwartz Class. D. The Fourier-Plancherel Transform. E. Hilbert Space. F. Formal Applications to Differential Equations. G. Bessel Functions. H. Special Results for n = 1. I. Hermite Polynomials. 14. Fourier Series in One Variable. A. Periodic Functions. B. Trigonometric Series. C. Fourier Coefficients. D. Convergence of Fourier Series. E. Summability of Fourier Series. F.A Counterexample. G. Parseval's Identity. H. Poisson Summation Formula. I.A Special Class of Sine Series --
15. Differentiation. A. The Vitali Covering Theorem. B. The Hardy-Littlewood Maximal Function. C. Lebesgue's Differentiation Theorem. D. The Lebesgue Set of a Function. E. Points of Density. F. Applications. G. The Vitali Covering Theorem (Again). H. The Besicovitch Covering Theorem. I. The Lebesgue Set of Order p. J. Change of Variables. K. Noninvertible Mappings --
16. Differentiation for Functions on R.A. Monotone Functions. B. Jump Functions. C. Another Theorem of Fubini. D. Bounded Variation. E. Absolute Continuity. F. Further Discussion of Absolute Continuity. G. Arc Length. H. Nowhere Differentiable Functions. I. Convex Functions.
Series Title: Jones and Bartlett books in mathematics.
Responsibility: Frank Jones.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/26211685> # Lebesgue integration on Euclidean space
    a schema:Book, schema:CreativeWork ;
    library:oclcnum "26211685" ;
    library:placeOfPublication <http://dbpedia.org/resource/Boston> ; # Boston
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/mau> ;
    schema:about <http://dewey.info/class/515.42/e20/> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/193709147#Thing/integral_calculus> ; # Integral calculus
    schema:about <http://experiment.worldcat.org/entity/work/data/193709147#Topic/lebesgue_mass> ; # Lebesgue-Maß
    schema:about <http://id.worldcat.org/fast/995240> ; # Lebesgue integral
    schema:about <http://experiment.worldcat.org/entity/work/data/193709147#Topic/malteori> ; # Målteori
    schema:about <http://experiment.worldcat.org/entity/work/data/193709147#Topic/lebesgue_integraler> ; # Lebesgue-integraler
    schema:about <http://experiment.worldcat.org/entity/work/data/193709147#Topic/euklidischer_raum> ; # Euklidischer Raum
    schema:about <http://id.worldcat.org/fast/1013175> ; # Measure theory
    schema:about <http://experiment.worldcat.org/entity/work/data/193709147#Topic/mesure_theorie_de_la> ; # Mesure, Théorie de la
    schema:about <http://experiment.worldcat.org/entity/work/data/193709147#Topic/lebesgue_integrale_de> ; # Lebesgue, Intégrale de
    schema:bookFormat bgn:PrintBook ;
    schema:copyrightYear "1993" ;
    schema:creator <http://experiment.worldcat.org/entity/work/data/193709147#Person/jones_frank_1936> ; # Frank Jones
    schema:datePublished "1993" ;
    schema:description "14. Fourier Series in One Variable. A. Periodic Functions. B. Trigonometric Series. C. Fourier Coefficients. D. Convergence of Fourier Series. E. Summability of Fourier Series. F.A Counterexample. G. Parseval's Identity. H. Poisson Summation Formula. I.A Special Class of Sine Series -- 15. Differentiation. A. The Vitali Covering Theorem. B. The Hardy-Littlewood Maximal Function. C. Lebesgue's Differentiation Theorem. D. The Lebesgue Set of a Function. E. Points of Density. F. Applications. G. The Vitali Covering Theorem (Again). H. The Besicovitch Covering Theorem. I. The Lebesgue Set of Order p. J. Change of Variables. K. Noninvertible Mappings -- 16. Differentiation for Functions on R.A. Monotone Functions. B. Jump Functions. C. Another Theorem of Fubini. D. Bounded Variation. E. Absolute Continuity. F. Further Discussion of Absolute Continuity. G. Arc Length. H. Nowhere Differentiable Functions. I. Convex Functions."@en ;
    schema:description "9. The Gamma Function. A. Definition and Simple Properties. B. Generalization. C. The Measure of Balls. D. Further Properties of the Gamma Function. E. Stirling's Formula. F. The Gamma Function on R -- 10. L[superscript p] Spaces. A. Definition and Basic Inequalities. B. Metric Spaces and Normed Spaces. C. Completeness of L[superscript p]. D. The Case p = [actual symbol not reproducible]. E. Relations between L[superscript p] Spaces. F. Approximation by C[actual symbol not reproducible](R[superscript n]). G. Miscellaneous Problems. H. The Case 0

"@en ;
    schema:description "1. Introduction to R[superscript n]. A. Sets. B. Countable Sets. C. Topology. D. Compact Sets. E. Continuity. F. The Distance Function -- 2. Lebesgue Measure on R[superscript n]. A. Construction. B. Properties of Lebesgue Measure. C. Appendix: Proof of P1 and P2 -- 3. Invariance of Lebesgue Measure. A. Some Linear Algebra. B. Translation and Dilation. C. Orthogonal Matrices. D. The General Matrix -- 4. Some Interesting Sets. A.A Nonmeasurable Set. B.A Bevy of Cantor Sets. C. The Lebesgue Function. D. Appendix: The Modulus of Continuity of the Lebesgue Functions -- 5. Algebras of Sets and Measurable Functions. A. Algebras and [sigma]-Algebras. B. Borel Sets. C.A Measurable Set which Is Not a Borel Set. D. Measurable Functions. E. Simple Functions -- 6. Integration. A. Nonnegative Functions. B. General Measurable Functions. C. Almost Everywhere. D. Integration Over Subsets of R[superscript n]. E. Generalization: Measure Spaces. F. Some Calculations. G. Miscellany -- 7. Lebesgue Integral on R[superscript n]. A. Riemann Integral. B. Linear Change of Variables. C. Approximation of Functions in L[superscript 1]. D. Continuity of Translation L[superscript 1] -- 8. Fubini's Theorem for R[superscript n]."@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/193709147> ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/193709147#Series/jones_and_bartlett_books_in_mathematics> ; # Jones and Bartlett books in mathematics.
    schema:isSimilarTo <http://www.worldcat.org/oclc/765609957> ;
    schema:name "Lebesgue integration on Euclidean space"@en ;
    schema:productID "26211685" ;
    schema:publication <http://www.worldcat.org/title/-/oclc/26211685#PublicationEvent/boston_jones_and_bartlett_1993> ;
    schema:publisher <http://experiment.worldcat.org/entity/work/data/193709147#Agent/jones_and_bartlett> ; # Jones and Bartlett
    schema:workExample <http://worldcat.org/isbn/9780867202038> ;
    umbel:isLike <http://bnb.data.bl.uk/id/resource/GB9362932> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/26211685> ;
    .


Related Entities

<http://dbpedia.org/resource/Boston> # Boston
    a schema:Place ;
    schema:name "Boston" ;
    .

<http://experiment.worldcat.org/entity/work/data/193709147#Agent/jones_and_bartlett> # Jones and Bartlett
    a bgn:Agent ;
    schema:name "Jones and Bartlett" ;
    .

<http://experiment.worldcat.org/entity/work/data/193709147#Person/jones_frank_1936> # Frank Jones
    a schema:Person ;
    schema:birthDate "1936" ;
    schema:familyName "Jones" ;
    schema:givenName "Frank" ;
    schema:name "Frank Jones" ;
    .

<http://experiment.worldcat.org/entity/work/data/193709147#Series/jones_and_bartlett_books_in_mathematics> # Jones and Bartlett books in mathematics.
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/26211685> ; # Lebesgue integration on Euclidean space
    schema:name "Jones and Bartlett books in mathematics." ;
    schema:name "Jones and Bartlett books in mathematics" ;
    .

<http://experiment.worldcat.org/entity/work/data/193709147#Thing/integral_calculus> # Integral calculus
    a schema:Thing ;
    schema:name "Integral calculus" ;
    .

<http://experiment.worldcat.org/entity/work/data/193709147#Topic/euklidischer_raum> # Euklidischer Raum
    a schema:Intangible ;
    schema:name "Euklidischer Raum"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/193709147#Topic/lebesgue_integrale_de> # Lebesgue, Intégrale de
    a schema:Intangible ;
    schema:name "Lebesgue, Intégrale de"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/193709147#Topic/lebesgue_integraler> # Lebesgue-integraler
    a schema:Intangible ;
    schema:name "Lebesgue-integraler"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/193709147#Topic/mesure_theorie_de_la> # Mesure, Théorie de la
    a schema:Intangible ;
    schema:name "Mesure, Théorie de la"@en ;
    .

<http://id.worldcat.org/fast/1013175> # Measure theory
    a schema:Intangible ;
    schema:name "Measure theory"@en ;
    .

<http://id.worldcat.org/fast/995240> # Lebesgue integral
    a schema:Intangible ;
    schema:name "Lebesgue integral"@en ;
    .

<http://worldcat.org/isbn/9780867202038>
    a schema:ProductModel ;
    schema:isbn "0867202033" ;
    schema:isbn "9780867202038" ;
    .

<http://www.worldcat.org/oclc/765609957>
    a schema:CreativeWork ;
    rdfs:label "Lebesgue integration on Euclidean space." ;
    schema:description "Online version:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/26211685> ; # Lebesgue integration on Euclidean space
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.