Weak and q-weak variationalmeasures defined by Brian S. Thomson [On VBG functions and the Denjoy–Khintchine integral, Real Analysis Exchange, 41(1) (2015/16), 173–226] are shown to coincide with variational measures resulting from Riemann definitions of some wide Denjoy type integrals. This fact is applied in characterizations of these integrals, via absolute continuity of weak and q-weak measures. In related results, it is discussed if these Riemann definitions can be essentially simplified. The paper is a follow-up to a paper by the author published some time ago in the Rendiconti [On Riemann-type definition for the wide Denjoy integral, Rendiconti del Seminario Matematico della Università di Padova, 126 (2011), 175–200].
DOI : 10.4171/RSMUP/27
Mots clés : Wide Denjoy integral, weak variational measure, composite gauge, local system, VBG, ACG, Lusin’s condition /$N$)
@article{RSMUP_2019__142__9_0,
author = {Sworowski, Piotr},
title = {On some variational measures related to the wide {Denjoy} integral and its counterparts},
journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
pages = {9--36},
publisher = {European Mathematical Society Publishing House},
address = {Zuerich, Switzerland},
volume = {142},
year = {2019},
doi = {10.4171/RSMUP/27},
mrnumber = {4032801},
zbl = {1448.26012},
url = {http://archive.numdam.org/articles/10.4171/RSMUP/27/}
}
TY - JOUR AU - Sworowski, Piotr TI - On some variational measures related to the wide Denjoy integral and its counterparts JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2019 SP - 9 EP - 36 VL - 142 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://archive.numdam.org/articles/10.4171/RSMUP/27/ DO - 10.4171/RSMUP/27 ID - RSMUP_2019__142__9_0 ER -
%0 Journal Article %A Sworowski, Piotr %T On some variational measures related to the wide Denjoy integral and its counterparts %J Rendiconti del Seminario Matematico della Università di Padova %D 2019 %P 9-36 %V 142 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://archive.numdam.org/articles/10.4171/RSMUP/27/ %R 10.4171/RSMUP/27 %F RSMUP_2019__142__9_0
Sworowski, Piotr. On some variational measures related to the wide Denjoy integral and its counterparts. Rendiconti del Seminario Matematico della Università di Padova, Tome 142 (2019), pp. 9-36. doi : 10.4171/RSMUP/27. http://archive.numdam.org/articles/10.4171/RSMUP/27/
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