On a certain pair of measures on $\ell _p$
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E. A. Riss
Translated by: the author - St. Petersburg Math. J. 25 (2014), 105-115
- DOI: https://doi.org/10.1090/S1061-0022-2013-01281-7
- Published electronically: November 20, 2013
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Abstract:
A pair of finite Borel measures $\mu$ and $\nu$ on $\ell _p$, $1\le p< \infty$, $\mu \ne \nu$, is constructed so that the identity $\mu (B(x,r))=\nu (B(x,r))$ is fulfilled for all balls $B(x,r)$ with centers $x \in \ell _p$ and radii $r<R(x)$, where $R(x)>0$ for a.e. $x$.References
- D. Preiss and J. Tišer, Measures in Banach spaces are determined by their values on balls, Mathematika 38 (1991), no. 2, 391–397 (1992). MR 1147839, DOI 10.1112/S0025579300006744
- E. A. Riss, Measures that coincide on balls, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 177 (1989), no. Problemy Teorii Veroyatnost. Raspred. XI, 122–128, 190 (Russian). MR 1053134
- Roy O. Davies, Measures not approximable or not specifiable by means of balls, Mathematika 18 (1971), 157–160. MR 310162, DOI 10.1112/S0025579300005386
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Bibliographic Information
- E. A. Riss
- Affiliation: Hertzen Russia State Pedagogical University, Moika 48, St. Petersburg 191186, Russia
- Email: e.riss@bk.ru
- Received by editor(s): May 4, 2012
- Published electronically: November 20, 2013
- © Copyright 2013 American Mathematical Society
- Journal: St. Petersburg Math. J. 25 (2014), 105-115
- MSC (2010): Primary 28C20
- DOI: https://doi.org/10.1090/S1061-0022-2013-01281-7
- MathSciNet review: 3113430