A new scale-invariant geometry on L1 spaces

Dress A, Lokot T, Pustyl'nikov LD (2004)
Applied Mathematics Letters 17(7): 815-820.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Dress, AndreasUniBi; Lokot, TatianaUniBi; Pustyl'nikov, Lev Davidovich
Abstract / Bemerkung
Nieto, Torres and Vazquez-Trasande recently considered, for any n is an element of N, the bivariate map and showed that this map satisfies the triangle inequality. Here, we suggest to consider, more generally, for any space X with a positive measure mu, the bivariate map and show that, for nonnegative maps p, q is an element of L, (X, p), the length of a geodesic (relative to d) coincides with the sum In particular, a continuous path S : [0, 1] --> L-1 (X, mu)(+) : t --> S-t is a geodesic in L-1 (X, mu) relative to this metric if and only if there exists some t(0) is an element of [0, 1] with St(0) = max(p, q), and one has S-t < S-t', for all t, t' is an element of [0, t(o)] with t less than or equal to t' and for all t, t' is an element of [t(0), 1] with t greater than or equal to t'. (C) 2004 Elsevier Ltd. All rights reserved.
Stichworte
scale invariance; L-1 space; geodesics; triangle inequality; L-1 geometry; NTV-metric
Erscheinungsjahr
2004
Zeitschriftentitel
Applied Mathematics Letters
Band
17
Ausgabe
7
Seite(n)
815-820
ISSN
0893-9659
Page URI
https://pub.uni-bielefeld.de/record/1607203

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Dress A, Lokot T, Pustyl'nikov LD. A new scale-invariant geometry on L1 spaces. Applied Mathematics Letters. 2004;17(7):815-820.
Dress, A., Lokot, T., & Pustyl'nikov, L. D. (2004). A new scale-invariant geometry on L1 spaces. Applied Mathematics Letters, 17(7), 815-820. https://doi.org/10.1016/j.aml.2004.06.011
Dress, A., Lokot, T., and Pustyl'nikov, L. D. (2004). A new scale-invariant geometry on L1 spaces. Applied Mathematics Letters 17, 815-820.
Dress, A., Lokot, T., & Pustyl'nikov, L.D., 2004. A new scale-invariant geometry on L1 spaces. Applied Mathematics Letters, 17(7), p 815-820.
A. Dress, T. Lokot, and L.D. Pustyl'nikov, “A new scale-invariant geometry on L1 spaces”, Applied Mathematics Letters, vol. 17, 2004, pp. 815-820.
Dress, A., Lokot, T., Pustyl'nikov, L.D.: A new scale-invariant geometry on L1 spaces. Applied Mathematics Letters. 17, 815-820 (2004).
Dress, Andreas, Lokot, Tatiana, and Pustyl'nikov, Lev Davidovich. “A new scale-invariant geometry on L1 spaces”. Applied Mathematics Letters 17.7 (2004): 815-820.

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