G. BOUCHITTÉ, T. CHAMPION and C. JIMEMEZ
Completion of the space of measures in the Kantorovich norm
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 IRd with respect to the Monge-Kantorovich norm. This extends the well known case d=1 (see ). Different issues connected with the existence of Monge dual potentials and tangent spaces to measures (see , , ) are also discussed.