On a Space of Besicovitch Functions
Result description
Let C([0,1]) be the set of all continuous functions mapping the unit interval [0,1] into itself, equipped by the metric rho of uniform convergence (and the induced topology tau). A function fin C([0,1]) is called Besicovitch if it has nowhere one-sided derivative (finite of infinite). For the Lebesgue measure lambda we define the set B(lambda)subset C([0,1]) by B(lambda)={fvert~forall~text{Borel}~Asubset [0,1]colon~lambda(A)=lambda(f^{-1}(A))text{ and }ftext{ is Besicovitch}}. We construct a set Xsubset B(lambda) such that the space (X,tauvert X) is homemorphic to the product topological space (prod_{i=0}^{infty}[0,1),mu).
Keywords
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
On a Space of Besicovitch Functions
Original language description
Let C([0,1]) be the set of all continuous functions mapping the unit interval [0,1] into itself, equipped by the metric rho of uniform convergence (and the induced topology tau). A function fin C([0,1]) is called Besicovitch if it has nowhere one-sided derivative (finite of infinite). For the Lebesgue measure lambda we define the set B(lambda)subset C([0,1]) by B(lambda)={fvert~forall~text{Borel}~Asubset [0,1]colon~lambda(A)=lambda(f^{-1}(A))text{ and }ftext{ is Besicovitch}}. We construct a set Xsubset B(lambda) such that the space (X,tauvert X) is homemorphic to the product topological space (prod_{i=0}^{infty}[0,1),mu).
Czech name
O prostoru Besikovičových funkcí
Czech description
V článku je zkonstruován podprostor X prostoru C([0,1]) s vlastnostmi:1) X obsahuje Besikovičovy funkce, 2) každá funkce z X zachovává Lebesgueovu míru, 3) X je homeomorfní s prostorem [0,1]^{alef_0}.
Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2005
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Real Analysis Exchange
ISSN
0147-1937
e-ISSN
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Volume of the periodical
30
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
10
Pages from-to
173-182
UT code for WoS article
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EID of the result in the Scopus database
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Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2005