In a metric space (X, d) we reconstruct an approximation of a Borel measure µ starting from a premeasure q defined on the collection of closed balls, and such that q approximates the values of µ on these balls. More precisely, under a geometric assumption on the distance ensuring a Besicovitch covering property, and provided that there exists a Borel measure on X satisfying an asymptotic doubling-type condition, we show that a suitable packing construction produces a measure µˆq which is equivalent to µ. Moreover we show the stability of this process with respect to the accuracy of the initial approximation. We also investigate the case of signed measures.

Recovering measures from approximate values on balls / Buet, Blanche; Leonardi, Gian Paolo. - In: ANNALES ACADEMIAE SCIENTIARUM FENNICAE. MATHEMATICA. - ISSN 1798-2383. - ELETTRONICO. - 41:(2016), pp. 947-972. [10.5186/aasfm.2016.4160]

Recovering measures from approximate values on balls

LEONARDI, Gian Paolo
2016

Abstract

In a metric space (X, d) we reconstruct an approximation of a Borel measure µ starting from a premeasure q defined on the collection of closed balls, and such that q approximates the values of µ on these balls. More precisely, under a geometric assumption on the distance ensuring a Besicovitch covering property, and provided that there exists a Borel measure on X satisfying an asymptotic doubling-type condition, we show that a suitable packing construction produces a measure µˆq which is equivalent to µ. Moreover we show the stability of this process with respect to the accuracy of the initial approximation. We also investigate the case of signed measures.
2016
41
947
972
Recovering measures from approximate values on balls / Buet, Blanche; Leonardi, Gian Paolo. - In: ANNALES ACADEMIAE SCIENTIARUM FENNICAE. MATHEMATICA. - ISSN 1798-2383. - ELETTRONICO. - 41:(2016), pp. 947-972. [10.5186/aasfm.2016.4160]
Buet, Blanche; Leonardi, Gian Paolo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1115901
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