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On the uniform strong Lusin condition

In: Mathematica Slovaca, vol. 63, no. 2
Piotr Sworowski
Detaily:
Rok, strany: 2013, 229 - 242
Kľúčové slová:
Kurzweil-Henstock integral, $\ACGd$, Strong Lusin Condition, variational measure, \textsl{VBG}, \textsl{ACG}, equiintegrability, Alexiewicz norm
O článku:
Assume that $f$ is a function defined on some interval $I\subset\mathbb Rm$. Literature offers several equivalences of the type: $f$ has a property \texttt{P} (like absolute continuity, bounded variation, etc.) on $I$ if and only if $f$ has \texttt{P} on each (closed) null subset of $I$. Such results feature a pretty important role in the integration theory. We make a brief review of these results and then provide an example showing that they can break down if considered in the uniform version, that is, for sequences of functions instead of a particular function.
Ako citovať:
ISO 690:
Sworowski, P. 2013. On the uniform strong Lusin condition. In Mathematica Slovaca, vol. 63, no.2, pp. 229-242. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0095-9

APA:
Sworowski, P. (2013). On the uniform strong Lusin condition. Mathematica Slovaca, 63(2), 229-242. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0095-9
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