The Lebesgue differentiation theorem revisited
We prove a general version of the Lebesgue differentiation theorem where the averages are taken on a family of sets that may not shrink nicely to any point. These families of sets involve the unit ball and its dilated by negative integers of an expansive linear map. We also give a characterization o...
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Published in | Expositiones mathematicae Vol. 37; no. 3; pp. 322 - 332 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier GmbH
01.09.2019
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Subjects | |
Online Access | Get full text |
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Summary: | We prove a general version of the Lebesgue differentiation theorem where the averages are taken on a family of sets that may not shrink nicely to any point. These families of sets involve the unit ball and its dilated by negative integers of an expansive linear map. We also give a characterization of the Lebesgue measurable functions on Rn in terms of approximate continuity associated to an expansive linear map. |
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ISSN: | 0723-0869 1878-0792 |
DOI: | 10.1016/j.exmath.2019.02.001 |