Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 50, No. 1, pp. 295-299 (2009)
$I$-measures in Minkowski planes
Andreas FankhänelFaculty of Mathematics, University of Technology Chemnitz, 09107 Chemnitz, Germany
Abstract: Let $\mu$ be an angular measure in a $2$-dimensional normed linear space (i.e., in a Minkowski plane). We consider certain measures $\mu$, called $I$-measures, and show that their existence is sufficient for the plane to be Euclidean.
Keywords: angular measure, Birkhoff orthogonality, inner product space, James orthogonality, normed plane, Theorem of Thales
Classification (MSC2000): 46B20, 46C15, 52A21
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Electronic version published on: 29 Dec 2008. This page was last modified: 28 Jan 2013.