Siberian Mathematical Journal

, Volume 53, Issue 6, pp 984–995 | Cite as

Quasispaces induced by vector fields measurable in ℝ3

  • A. V. Belykh
  • A. V. Greshnov


We study some metric functions that are induced by a class of basis vector fields in ℝ3 with measurable coordinates. These functions are proved to be quasimetrics in the domain of definition of the vector fields. Under some natural constraints, the Rashevsky-Chow Theorem and the Ball-Box Theorem are established for the classes of vector fields we consider.


vector field quasimetric generalized triangle inequality horizontal curve 


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© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirsk State UniversityNovosibirskRussia

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