On the Wasserstein distance between mutually singular measures
On the Wasserstein distance between mutually singular measures
Abstract We study the Wasserstein distance between two measures <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>μ</m:mi> <m:mo>,</m:mo> <m:mi>ν</m:mi> </m:mrow> </m:math> {\mu,\nu} which are mutually singular. In particular, we are interested in minimization problems of the form <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mrow> <m:mi>W</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>μ</m:mi> <m:mo>,</m:mo> <m:mi mathvariant="script">𝒜</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> …