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• W1546802176 abstract "Motivated by recent developments on calculus in metric measure spaces $(X,mathrm d,mathrm m)$, we prove a general duality principle between Fuglede's notion [15] of $p$-modulus for families of finite Borel measures in $(X,mathrm d)$ and probability measures with barycenter in $L^q(X,mathrm m)$, with $q$ dual exponent of $pin (1,infty)$. We apply this general duality principle to study null sets for families of parametric and non-parametric curves in $X$. In the final part of the paper we provide a new proof, independent of optimal transportation, of the equivalence of notions of weak upper gradient based on $p$-podulus [21, 23] and suitable probability measures in the space of curves ([6, 7])." @default.
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• W1546802176 date "2015-01-01" @default.
• W1546802176 modified "2023-10-10" @default.
• W1546802176 title "On the duality between $p$-modulus and probability measures" @default.
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• W1546802176 doi "https://doi.org/10.4171/jems/546" @default.
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