On McShane integrability of Banach space-valued functions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F04%3A00106904" target="_blank" >RIV/67985840:_____/04:00106904 - isvavai.cz</a>
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 McShane integrability of Banach space-valued functions
Original language description
The McShane integral of Banach space-valued functions f:I..X defined on an m-dimensional interval I is considered in this paper. We show that a McShane integrable function is integrable over measurable sets contained in I (Theorem 9 ). A certain type ofabsolute continuity of the indefinite McShane integral with respect to Lebesgue measure is derived (Theorem 11) and we show that the indefinite McShane integral is countably additive (Theorem 16)). Allowing more general partitions using measurable sets instead of intervals another McShane type integral is defined and we show that it is equivalent to the original McShane integral (Theorem 21).
Czech name
McShaneova integrovatelnost funkcí s hodnotami v Banachově prostoru
Czech description
Vyšetřuje se McShaneův integrál funkcí f:I X definovaných na m-rozměrném intervalu s hodnotami v Banachově prostoru. Je dokázáno, že McShaneovsky integrovatelná funkce je integrovatelná na měřitelných množinách v I. ( věta 9 ). Odvozuje se jistý druh absolutní spojitosti neurčité k McShaneovu integrálu vzhledem k Lebesgueově míře ( věta 11 ) a ukazuje se, že platí konvergenční věta Vitaliova typu.
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA201%2F01%2F1199" target="_blank" >GA201/01/1199: Summation integral and its application in equation theory</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2004
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
29
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
18
Pages from-to
763-780
UT code for WoS article
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EID of the result in the Scopus database
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