By using the property known as Federer-Fleming conjecture (cf. [7, 3.1.17]), recently resolved by B. Bojarski, we prove the following Lusin type result: Theorem. Let A Rn be a measurable set and let k be a nonnegative integer. Assume that to each x 2 A corresponds a polynomial Px : Rn ! R of degree less or equal to k + 1 such that ap lim x!a (Formula Presented) We will use such a theorem to provide a simple new proof of a well-known property of Sobolev functions.
A lusin type result / Delladio, Silvano. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 19:6(2020), pp. 3083-3091. [10.3934/CPAA.2020133]
A lusin type result
Delladio, Silvano
2020-01-01
Abstract
By using the property known as Federer-Fleming conjecture (cf. [7, 3.1.17]), recently resolved by B. Bojarski, we prove the following Lusin type result: Theorem. Let A Rn be a measurable set and let k be a nonnegative integer. Assume that to each x 2 A corresponds a polynomial Px : Rn ! R of degree less or equal to k + 1 such that ap lim x!a (Formula Presented) We will use such a theorem to provide a simple new proof of a well-known property of Sobolev functions.| File | Dimensione | Formato | |
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