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Angular measures and Birkhoff orthogonality in Minkowski planes

Naszódi, Márton, Prokaj, Vilmos and Swanepoel, Konrad ORCID: 0000-0002-1668-887X (2020) Angular measures and Birkhoff orthogonality in Minkowski planes. Aequationes Mathematicae. ISSN 0001-9054

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Identification Number: 10.1007/s00010-020-00715-4

Abstract

Let x and y be two unit vectors in a normed plane R 2. We say that x is Birkhoff orthogonal to y if the line through x in the direction y supports the unit disc. A B-measure (Fankhänel in Beitr Algebra Geom 52(2):335–342, 2011) is an angular measure μ on the unit circle for which μ(C) = π/ 2 whenever C is a shorter arc of the unit circle connecting two Birkhoff orthogonal points. We present a characterization of the normed planes that admit a B-measure.

Item Type: Article
Official URL: https://link.springer.com/journal/10
Additional Information: © 2020 The Authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 07 Feb 2020 17:18
Last Modified: 20 Jul 2020 23:30
URI: http://eprints.lse.ac.uk/id/eprint/103319

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