An abstract and generalized approach to the Vitali theorem on nonmeasurable sets

Sanjib Basu; Debasish Sen

Mathematica Bohemica (2020)

  • Volume: 145, Issue: 1, page 65-70
  • ISSN: 0862-7959

Abstract

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Here we present abstract formulations of two theorems of Solecki which deal with some generalizations of the classical Vitali theorem on nonmeasurable sets in spaces with transformation groups.

How to cite

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Basu, Sanjib, and Sen, Debasish. "An abstract and generalized approach to the Vitali theorem on nonmeasurable sets." Mathematica Bohemica 145.1 (2020): 65-70. <http://eudml.org/doc/297088>.

@article{Basu2020,
abstract = {Here we present abstract formulations of two theorems of Solecki which deal with some generalizations of the classical Vitali theorem on nonmeasurable sets in spaces with transformation groups.},
author = {Basu, Sanjib, Sen, Debasish},
journal = {Mathematica Bohemica},
keywords = {spaces with transformation groups; $k$-additive measurable structure; $k$-small system; upper semicontinuous $k$-small system; $k$-additive algebra admissible with respect to a $k$-small system},
language = {eng},
number = {1},
pages = {65-70},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An abstract and generalized approach to the Vitali theorem on nonmeasurable sets},
url = {http://eudml.org/doc/297088},
volume = {145},
year = {2020},
}

TY - JOUR
AU - Basu, Sanjib
AU - Sen, Debasish
TI - An abstract and generalized approach to the Vitali theorem on nonmeasurable sets
JO - Mathematica Bohemica
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 145
IS - 1
SP - 65
EP - 70
AB - Here we present abstract formulations of two theorems of Solecki which deal with some generalizations of the classical Vitali theorem on nonmeasurable sets in spaces with transformation groups.
LA - eng
KW - spaces with transformation groups; $k$-additive measurable structure; $k$-small system; upper semicontinuous $k$-small system; $k$-additive algebra admissible with respect to a $k$-small system
UR - http://eudml.org/doc/297088
ER -

References

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  10. Riečan, B., Neubrunn, T., 10.1007/978-94-015-8919-2, Mathematics and Its Applications 411. Kluwer Academic Publisher, Dordrecht (1997). (1997) Zbl0916.28001MR1489521DOI10.1007/978-94-015-8919-2
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  12. Solecki, S., 10.2307/2160530, Proc. Am. Math. Soc. 119 (1993), 897-902. (1993) Zbl0795.28010MR1152992DOI10.2307/2160530
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  14. Vitali, G., Sul problema della misura dei gruppi di punti di una retta. Nota, Gamberini e Parmeggiani, Bologna (1905), Italian 9999JFM99999 36.0586.03. (1905) 

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