Geodesic
An abstract and generalized formulation of a theorem by Pelc and Prikry on invariant extension of Borel measure
Filomat, Tome 36 (2022) no. 8, p. 2711

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DOI

There are certain countably generated σ-algebras of sets in the real line which do not admit any non-zero, σ-finite, diffused (or, continuous) measure. Such countably generated σ-algebras can be obtained by the use of some special types of infinite matrix known as the Banach-Kuratowski matrix and the same may be used in deriving a generalized version of Pelc and Prikry's theorem as shown by Kharazishvili. Here, in this paper, we develop an abstract and generalized formulation of Pelc and Prikry's theorem in spaces with transformation groups, where instead of using measure type functionals as done by Kharazishvili, we utilize a newly introduced concept which is that of an admissible, diffused k-additive algebra where k is an arbitrary infinite cardinal.
DOI : 10.2298/FIL2208711B
Classification : 28A05, 28D05, 28D99
Keywords: Banach Kuratowski Matrix, diffused admissible functional, transformation group, regular admissible k-additive algebra, k-chain condition, generalized continuum hypothesis, absolutely nonmeasurable function 
Sanjib Basu; Debasish Sen. An abstract and generalized formulation of a theorem by Pelc and Prikry on invariant extension of Borel measure. Filomat, Tome 36 (2022) no. 8, p. 2711 . doi: 10.2298/FIL2208711B
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     title = {An abstract and generalized formulation of a theorem by {Pelc} and {Prikry} on invariant extension of {Borel} measure},
     journal = {Filomat},
     pages = {2711 },
     year = {2022},
     volume = {36},
     number = {8},
     doi = {10.2298/FIL2208711B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2208711B/}
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