Subsets of the Plane with Small Linear Sections and Invariant Extensions of the Two-Dimensional Lebesgue Measure

Author： Kharazishvili A.  

Publisher： Springer Publishing Company

ISSN： 1072-947X

Source： Georgian Mathematical Journal, Vol.06, Iss.5, 1999-09, pp. : 441-446

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Abstract

We consider some subsets of the Euclidean plane R2, having small linear sections (in all directions), and investigate those sets from the point of view of measurability with respect to certain invariant extensions of the classical Lebesgue measure on R2.

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