The paper proposes Choquet extensions for set-pair functions and L^p-integrated global extension constants, proving a monotonicity inequality that unifies Cheeger, spectral, and isoperimetric bounds across graph limits, hypergraphs, manifolds, and metric measure spaces.
Chayes, L´ aszl´ o Lov´ asz, Vera T
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Choquet-type extension theory of set-pair functions, and applications to graph limits, hypergraphs, Riemannian manifolds and metric measure spaces
The paper proposes Choquet extensions for set-pair functions and L^p-integrated global extension constants, proving a monotonicity inequality that unifies Cheeger, spectral, and isoperimetric bounds across graph limits, hypergraphs, manifolds, and metric measure spaces.