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An injective Borel measurable map preserving fixed cross-ratio up to complex conjugation is a Möbius map

T. A. Kergilova

Gorno-Altaisk State University

Abstract: The paper presents criterion for Möbius mappings in the complex plane: if an injective Borel measurable map preserves fixed cross-ratio $\lambda\notin \{0, 1, \infty\}$ up to complex conjugation, then it is a Möbius map.

Keywords: Moebius transformation, cross-ratio, linear-fractional map, extended complex plane, complex conjugation, Borel measurability.

UDC: 517.54

Received: 08.06.2010