Homeomorphisms of Flat Areas With Conservation Condition Measures
Year: 2025
Type: article
Abstract: The paper establishes conditions for the open set 𝑋 ⊂ R2 under which the homeomorphism 𝐹 : 𝑋 → R2, which preserves the measure of any closed unit square and any closed unit semidisk of 𝑋, preserves the measure of any Lebesgue measurable subset of 𝑋. It is also shown that the established conditions cannot be significantly weakened.
Authors: Volchkov, V. V., Pilipenko, I. S.
Institution: Institute of Applied Mathematics and Mechanics
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7083672889
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