skip to content
Measure and category : a survey of the analogies between topological and measure spaces Preview this item
ClosePreview this item

Measure and category : a survey of the analogies between topological and measure spaces

Author: John C Oxtoby
Publisher: New York : Springer-Verlag, ©1980.
Series: Graduate texts in mathematics, 2.
Edition/Format:   Print book : English : 2d edView all editions and formats

Oxtoby Bryn Mawr, April 1980 Preface to the First Edition This book has two main themes: the Baire category theorem as a method for proving existence, and the "duality" between measure and category.


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

More like this


Find a copy online

Links to this item

Find a copy in the library

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


Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: John C Oxtoby
ISBN: 0387905081 9780387905082 3540905081 9783540905080
OCLC Number: 6331238
Description: ix, 106 pages ; 24 cm.
Contents: 1. Measure and Category on the Line.- Countable sets, sets of first category, nullsets, the theorems of Cantor, Baire and Borel.- 2. Liouville Numbers.- Algebraic and transcendental numbers, measure and category of the set of Liouville numbers.- 3. Lebesgue Measure in r-Space.- Definitions and principal properties, measurable sets, the Lebesgue density theorem.- 4. The Property of Baire.- Its analogy to measurability, properties of regular open sets.- 5. Non-Measurable Sets.- Vitali sets, Bernstein sets, Ulam's theorem, inaccessible cardinals, the continuum hypothesis.- 6. The Banach-Mazur Game.- Winning strategies, category and local category, indeterminate games.- 7. Functions of First Class.- Oscillation, the limit of a sequence of continuous functions, Riemann integrability.- 8. The Theorems of Lusin and Egoroff.- Continuity of measurable functions and of functions having the property of Baire, uniform convergence on subsets.- 9. Metric and Topological Spaces.- Definitions, complete and topologically complete spaces, the Baire category theorem.- 10. Examples of Metric Spaces.- Uniform and integral metrics in the space of continuous functions, integrable functions, pseudo-metric spaces, the space of measurable sets.- 11. Nowhere Differentiable Functions.- Banach's application of the category method.- 12. The Theorem of Alexandroff.- Remetrization of a G? subset, topologically complete subspaces.- 13. Transforming Linear Sets into Nullsets.- The space of automorphisms of an interval, effect of monotone substitution on Riemann integrability, nullsets equivalent to sets of first category.- 14. Fubini's Theorem.- Measurability and measure of sections of plane measurable sets.- 15. The Kuratowski-Ulam Theorem.- Sections of plane sets having the property of Baire, product sets, reducibility to Fubini's theorem by means of a product transformation.- 16. The Banach Category Theorem.- Open sets of first category or measure zero, Montgomery's lemma, the theorems of Marczewski and Sikorski, cardinals of measure zero, decomposition into a nullset and a set of first category.- 17. The Poincare Recurrence Theorem.- Measure and category of the set of points recurrent under a nondissipative transformation, application to dynamical systems.- 18. Transitive Transformations.- Existence of transitive automorphisms of the square, the category method.- 19. The Sierpinski-Erdoes Duality Theorem.- Similarities between the classes of sets of measure zero and of first category, the principle of duality.- 20. Examples of Duality.- Properties of Lusin sets and their duals, sets almost invariant under transformations that preserve nullsets or category.- 21. The Extended Principle of Duality.- A counter example, product measures and product spaces, the zero-one law and its category analogue.- 22. Category Measure Spaces.- Spaces in which measure and category agree, topologies generated by lower densities, the Lebesgue density topology.- Supplementary Notes and Remarks.- References.- Supplementary References.
Series Title: Graduate texts in mathematics, 2.
Responsibility: John C. Oxtoby.


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


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

<> # Measure and category : a survey of the analogies between topological and measure spaces
    a schema:Book, schema:CreativeWork ;
   library:oclcnum "6331238" ;
   library:placeOfPublication <> ; # New York
   library:placeOfPublication <> ;
   schema:about <> ; # Topologie
   schema:about <> ; # Measure theory
   schema:about <> ; # Catégories (Mathématiques)
   schema:about <> ; # Mesure, théorie de la
   schema:about <> ; # Maßtheorie
   schema:about <> ; # Espaces topologiques
   schema:about <> ; # Kategorie
   schema:about <> ; # Topological spaces
   schema:about <> ; # Spaces of measures
   schema:about <> ; # Categories (Mathematics)
   schema:about <> ;
   schema:bookEdition "2d ed." ;
   schema:bookFormat bgn:PrintBook ;
   schema:copyrightYear "1980" ;
   schema:creator <> ; # John C. Oxtoby
   schema:datePublished "1980" ;
   schema:exampleOfWork <> ;
   schema:inLanguage "en" ;
   schema:isPartOf <> ; # Graduate texts in mathematics ;
   schema:name "Measure and category : a survey of the analogies between topological and measure spaces"@en ;
   schema:productID "6331238" ;
   schema:publication <> ;
   schema:publisher <> ; # Springer-Verlag
   schema:url <> ;
   schema:workExample <> ;
   schema:workExample <> ;
   umbel:isLike <> ;
   wdrs:describedby <> ;

Related Entities

<> # New York
    a schema:Place ;
   schema:name "New York" ;

<> # Springer-Verlag
    a bgn:Agent ;
   schema:name "Springer-Verlag" ;

<> # Graduate texts in mathematics ;
    a bgn:PublicationSeries ;
   schema:hasPart <> ; # Measure and category : a survey of the analogies between topological and measure spaces
   schema:name "Graduate texts in mathematics ;" ;

<> # Catégories (Mathématiques)
    a schema:Intangible ;
   schema:name "Catégories (Mathématiques)"@en ;
   schema:name "Catégories (Mathématiques)"@fr ;

<> # Espaces topologiques
    a schema:Intangible ;
   schema:name "Espaces topologiques"@en ;
   schema:name "Espaces topologiques"@fr ;

<> # Mesure, théorie de la
    a schema:Intangible ;
   schema:name "Mesure, théorie de la"@en ;
   schema:name "Mesure, Théorie de la"@fr ;

<> # Measure theory
    a schema:Intangible ;
   schema:name "Measure theory"@en ;

<> # Spaces of measures
    a schema:Intangible ;
   schema:name "Spaces of measures"@en ;

<> # Topological spaces
    a schema:Intangible ;
   schema:name "Topological spaces"@en ;

<> # Categories (Mathematics)
    a schema:Intangible ;
   schema:name "Categories (Mathematics)"@en ;

<> # John C. Oxtoby
    a schema:Person ;
   schema:familyName "Oxtoby" ;
   schema:givenName "John C." ;
   schema:name "John C. Oxtoby" ;

    a schema:ProductModel ;
   schema:isbn "0387905081" ;
   schema:isbn "9780387905082" ;

    a schema:ProductModel ;
   schema:isbn "3540905081" ;
   schema:isbn "9783540905080" ;

    a genont:InformationResource, genont:ContentTypeGenericResource ;
   schema:about <> ; # Measure and category : a survey of the analogies between topological and measure spaces
   schema:dateModified "2017-12-23" ;
   void:inDataset <> ;

Content-negotiable representations

Close Window

Please sign in to WorldCat 

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