Some remarks on descriptive characterizations of the strong McShane integral

Sokol Bush Kaliaj

Mathematica Bohemica (2019)

  • Volume: 144, Issue: 4, page 339-355
  • ISSN: 0862-7959

Abstract

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We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function f : W → X defined on a non-degenerate closed subinterval W of ℝ m in terms of strong absolute continuity or, equivalently, in terms of McShane variational measure V ℳ F generated by the primitive F : ℐ W → X of f , where ℐ W is the family of all closed non-degenerate subintervals of W .

How to cite

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Kaliaj, Sokol Bush. "Some remarks on descriptive characterizations of the strong McShane integral." Mathematica Bohemica 144.4 (2019): 339-355. <http://eudml.org/doc/294701>.

@article{Kaliaj2019,
abstract = {We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function $f\colon W \rightarrow X$ defined on a non-degenerate closed subinterval $W$ of $\mathbb \{R\}^\{m\}$ in terms of strong absolute continuity or, equivalently, in terms of McShane variational measure $V_\{\mathcal \{M\}\} F$ generated by the primitive $F\colon \mathcal \{I\}_\{W\} \rightarrow X$ of $f$, where $\mathcal \{I\}_\{W\}$ is the family of all closed non-degenerate subintervals of $W$.},
author = {Kaliaj, Sokol Bush},
journal = {Mathematica Bohemica},
keywords = {strong McShane integral; McShane variational measure; Banach space; $m$-dimensional Euclidean space; compact non-degenerate $m$-dimensional interval},
language = {eng},
number = {4},
pages = {339-355},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some remarks on descriptive characterizations of the strong McShane integral},
url = {http://eudml.org/doc/294701},
volume = {144},
year = {2019},
}

TY - JOUR
AU - Kaliaj, Sokol Bush
TI - Some remarks on descriptive characterizations of the strong McShane integral
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 4
SP - 339
EP - 355
AB - We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function $f\colon W \rightarrow X$ defined on a non-degenerate closed subinterval $W$ of $\mathbb {R}^{m}$ in terms of strong absolute continuity or, equivalently, in terms of McShane variational measure $V_{\mathcal {M}} F$ generated by the primitive $F\colon \mathcal {I}_{W} \rightarrow X$ of $f$, where $\mathcal {I}_{W}$ is the family of all closed non-degenerate subintervals of $W$.
LA - eng
KW - strong McShane integral; McShane variational measure; Banach space; $m$-dimensional Euclidean space; compact non-degenerate $m$-dimensional interval
UR - http://eudml.org/doc/294701
ER -

References

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