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We examine some generalized densities (called (ψ, n)-densities) obtained as a result of strengthening the Lebesgue Density Theorem. It turns out that these notions are the generalizations of superdensity, enhanced density and m-density, and have some applications in the theory of sets of finite perimeter and in Sobolev spaces.

eISSN:
1338-9750
Language:
English
Publication timeframe:
3 times per year
Journal Subjects:
Mathematics, General Mathematics