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On Set Covariance and Three-Point Test Sets

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Abstract

The information contained in the measure of all shifts of two or three given points contained in an observed compact subset of \(\mathbb{R}^d \)is studied. In particular, the connection of the first order directional derivatives of the described characteristic with the oriented and the unoriented normal measure of a set representable as a finite union of sets with positive reach is established. For smooth convex bodies with positive curvatures, the second and the third order directional derivatives of the characteristic is computed.

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  1. Mathematical Institute of Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    J. Rataj

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  1. J. Rataj
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Rataj, J. On Set Covariance and Three-Point Test Sets. Czechoslovak Mathematical Journal 54, 205–214 (2004). https://doi.org/10.1023/B:CMAJ.0000027260.34288.7f

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  • DOI: https://doi.org/10.1023/B:CMAJ.0000027260.34288.7f

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