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Matsbornik-150: algebra, geometry, analysis
November 9, 2016 11:20–12:20, Moscow, Steklov Mathematical Institute, Conference hall, 9th floor
 


Virtual continuity

F. V. Petrov
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MP4 455.7 Mb
MP4 455.7 Mb

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F. V. Petrov
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Abstract: A classical theorem of Luzin states that a measurable function of one real variable is “almost” continuous. For measurable functions of several variables the analogous statement (continuity on a product of sets having almost full measure) does not hold in general. The search for a correct analogue of Luzin’s theorem leads to a notion of virtually continuous functions of several variables. We discuss virtually continuous functions and their applications to Kantorovich optimal transportation problem, Sobolev embedding theorems and operator theory.
 
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