Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 50, No. 1, pp. 295299 (2009) 

$I$measures in Minkowski planesAndreas FankhänelFaculty of Mathematics, University of Technology Chemnitz, 09107 Chemnitz, GermanyAbstract: 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 Full text of the article:
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