G. BOUCHITTÉ, T. CHAMPION and C. JIMEMEZ

Completion of the space of measures in the Kantorovich norm

Pages 127-139
Received: 21 April 2005   
Mathematics Subject Classification (2000): 49J45 - 46F05 - 46E15 - 46N10

Abstract: In this note we propose a new characterization of the completion of the set of balanced bounded measures compactly supported in IR^d with respect to the Monge-Kantorovich norm. This extends the well known case d=1 (see [6]). Different issues connected with the existence of Monge dual potentials and tangent spaces to measures (see [1], [3], [4]) are also discussed.