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Measure And Category by John C. Oxtoby

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1Duality Between Measure And Category In Uncountable Locally Compact Abelian Polish Groups

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We show that there is no addition preserving Erd\H{o}s-Sierpi\'nski mapping on any uncountable locally compact abelian Polish group. This generalizes results of Bartoszy\'nski and Kysiak.

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  • Title: ➤  Duality Between Measure And Category In Uncountable Locally Compact Abelian Polish Groups
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 4.14 Mbs, the file-s for this book were downloaded 135 times, the file-s went public at Sat Jul 20 2013.

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2Category-measure Duality: Convexity, Mid-point Convexity And Berz Sublinearity

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Category-measure duality concerns applications of Baire-category methods that have measure-theoretic analogues. The set-theoretic axiom needed in connection with the Baire category theorem is the Axiom of Dependent Choice DC rather than the Axiom of Choice AC. Berz used the Hahn-Banach Theorem over $\mathbb{Q}$ to prove that the graph of a measurable sublinear function that is $\mathbb{Q}_{+}$-homogeneous consists of two half-lines through the origin. We give a category form of the Berz theorem. Our proof is simpler than that of the classical measure-theoretic Berz theorem, our result contains Berz's theorem rather than simply being an analogue of it, and we use only DC rather than AC. Furthermore, the category form easily generalizes: the graph of a Baire sublinear function defined on a Banach space is a cone. The results are seen to be of automatic-continuity type. We use Christensen Haar null sets to extend the category approach beyond the locally compact setting where Haar measure exists. We extend Berz's result from Euclidean to Banach spaces, and beyond. Passing from sublinearity to convexity, we extend the Bernstein-Doetsch theorem and related continuity results, allowing our conditions to be `local' -- holding off some exceptional set.

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  • Title: ➤  Category-measure Duality: Convexity, Mid-point Convexity And Berz Sublinearity
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The book is available for download in "texts" format, the size of the file-s is: 0.36 Mbs, the file-s for this book were downloaded 21 times, the file-s went public at Fri Jun 29 2018.

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3Solovay Model And Duality Principle Between The Measure And The Baire Category In A Polish Topological Vector Space $H(X,S,\mu)$

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In Solovay model it is shown that the duality principle between the measure and the Baire category holds true with respect to the sentence - "The domain of an arbitrary generalized integral for a vector-function is of first category."

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  • Title: ➤  Solovay Model And Duality Principle Between The Measure And The Baire Category In A Polish Topological Vector Space $H(X,S,\mu)$
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The book is available for download in "texts" format, the size of the file-s is: 2.23 Mbs, the file-s for this book were downloaded 34 times, the file-s went public at Wed Jun 27 2018.

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4Measure And Category; A Survey Of The Analogies Between Topological And Measure Spaces

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In Solovay model it is shown that the duality principle between the measure and the Baire category holds true with respect to the sentence - "The domain of an arbitrary generalized integral for a vector-function is of first category."

“Measure And Category; A Survey Of The Analogies Between Topological And Measure Spaces” Metadata:

  • Title: ➤  Measure And Category; A Survey Of The Analogies Between Topological And Measure Spaces
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5Measure And Category : A Survey Of The Analogies Between Topological And Measure Spaces

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In Solovay model it is shown that the duality principle between the measure and the Baire category holds true with respect to the sentence - "The domain of an arbitrary generalized integral for a vector-function is of first category."

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  • Title: ➤  Measure And Category : A Survey Of The Analogies Between Topological And Measure Spaces
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 323.91 Mbs, the file-s for this book were downloaded 50 times, the file-s went public at Wed May 18 2022.

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6Invariants Of Measure And Category

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A survey of recent results concerning cardinal invariants of measure and category. Submitted as a chapter of the upcoming Handbook of Set Theory.

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  • Title: ➤  Invariants Of Measure And Category
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  • Language: English

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7Measure And Category : A Survey Of The Analogies Between Topological And Measure Spaces

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A survey of recent results concerning cardinal invariants of measure and category. Submitted as a chapter of the upcoming Handbook of Set Theory.

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  • Title: ➤  Measure And Category : A Survey Of The Analogies Between Topological And Measure Spaces
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 249.83 Mbs, the file-s for this book were downloaded 67 times, the file-s went public at Mon Jun 15 2020.

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8A Note On Duality Between Measure And Category

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A bijection from R to R is called an Erdos-Sierpinski mapping if it maps meager sets onto the first category sets and vice versa. We show that there is no Erdos-Sierpinski mapping preserving addition.

“A Note On Duality Between Measure And Category” Metadata:

  • Title: ➤  A Note On Duality Between Measure And Category
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 1.45 Mbs, the file-s for this book were downloaded 77 times, the file-s went public at Mon Sep 23 2013.

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9Monadic Second Order Logic With Measure And Category Quantifiers

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We investigate the extension of Monadic Second Order logic, interpreted over infinite words and trees, with generalized "for almost all" quantifiers interpreted using the notions of Baire category and Lebesgue measure.

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  • Title: ➤  Monadic Second Order Logic With Measure And Category Quantifiers
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The book is available for download in "texts" format, the size of the file-s is: 0.35 Mbs, the file-s for this book were downloaded 22 times, the file-s went public at Sat Jun 30 2018.

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10[ Graduate Texts In Mathematics] John C. Oxtoby Measure And Category A Survey Of The Analogies Between Topological And Measure Spaces 2nd Edition ( 2012, Springer) Libgen.li

math 3400 number theory textbook second edition

“[ Graduate Texts In Mathematics] John C. Oxtoby Measure And Category A Survey Of The Analogies Between Topological And Measure Spaces 2nd Edition ( 2012, Springer) Libgen.li” Metadata:

  • Title: ➤  [ Graduate Texts In Mathematics] John C. Oxtoby Measure And Category A Survey Of The Analogies Between Topological And Measure Spaces 2nd Edition ( 2012, Springer) Libgen.li
  • Language: English

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11Measure And Category [Elektronische Ressource] : A Survey Of The Analogies Between Topological And Measure Spaces

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math 3400 number theory textbook second edition

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  • Title: ➤  Measure And Category [Elektronische Ressource] : A Survey Of The Analogies Between Topological And Measure Spaces
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  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 43.43 Mbs, the file-s for this book were downloaded 1198 times, the file-s went public at Wed Dec 30 2015.

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1Measure and category

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“Measure and category” Metadata:

  • Title: Measure and category
  • Authors:
  • Languages: English - ger
  • Number of Pages: Median: 107
  • Publisher: ➤  Springer London, Limited - Springer - Springer-Verlag
  • Publish Date: ➤  
  • Publish Location: NewYork - New York - Berlin
  • Dewey Decimal Classification: 515.42
  • Library of Congress Classification: QA-0312.00000000QA-0312.00000000.O9 1980QA-0312.00000000.O9 1971QA-0331.50000000QA-0312.00000000.O915QA-0312.00000000.O9

“Measure and category” Subjects and Themes:

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First Setence:

"The notions of measure and category are based on that of countability."

Access and General Info:

  • First Year Published: 1971
  • Is Full Text Available: Yes
  • Is The Book Public: No
  • Access Status: Borrowable

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