Mathematica Bohemica, Vol. 145, No. 1, pp. 65-70, 2020


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

Sanjib Basu, Debasish Sen

Received October 14, 2017.   Published online January 2, 2019.

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.
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
Classification MSC:  28A05, 28D05


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Affiliations:   Sanjib Basu, Department of Mathematics, Bethune College, 181, Bidhan Sarani, Kolkata, West Bengal 700006, India, e-mail: sanjibbasu08@gmail.com; Debasish Sen, Saptagram Adarsha Vidyapith (High), Habra, 24 Parganas (North), West Bengal 743233, India, e-mail: reachtodebasish@gmail.com


 
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