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VIDEO LIBRARY |
Matsbornik-150: algebra, geometry, analysis
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Virtual continuity 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. |