Angular measures and Birkhoff orthogonality in Minkowski planes.

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.