6 papers · 1 filter
A few remarks on non-Baire sets in category bases
Sanjib Basu, Atasi Deb Ray, Abhit Chandra Pramanik
In this paper, we first establish some equivalent formulations of non-Baire sets in category bases. We then introduce the notion of an uniform non-Baire family of sets and show tha…
On non-Baire sets in category bases
Sanjib Basu, Atasi Deb Ray, Abhit Chandra Pramanik
In this paper, we prove a result on non-Baire sets in category bases which when applied together with a result of Grzegorek yeilds a comparatively stronger version of a decompositi…
On a theorem of Pelc and Prikry on the nonexistence of invariant extensions of Borel measures
Sanjib Basu, Debasish Sen
There are certain countably generated sigma-algebras of sets in the real line which do not admit any non-zero, sigma-finite, diffused (or, continuous) measure. Such countably gener…
On nonmeasurable subgroups in generalized measurable structures
S. Basu, D. Sen
In this paper, we prove a result on nonmeasurable subgroups in commutative Polish groups with respect to more generalized structures than sigma-finite measures.
On an abstract formulation of a theorem of Sierpinski
Debashish Sen, Sanjib Basu
In an earlier paper, we gave an abstract formulation of a theorem of Sierpiński in uncountable commutative groups. In this paper, we prove a result which generalizes the earlier fo…
A Nonseparable Invariant Extension of Lebesgue Measure -- A Generalized and Abstract Approach
Sanjib Basu, Debashish Sen
Here using some methods of combinatorial set theory, particularly the ones related to the construction of independent families of sets and some modified version of the notion of sm…