is -Liphschitz. c L fc L supf,g {∫ fdα + ∫ gdβ : f ⊕ g ≤ c, f, g ∈ 𝒞 } supf,g {∫ fdα + ∫ gdβ : f ⊕ g ≤ c, f, g ∈ LipL} replace by f gc replace by g fc Proposition (Ascoli-Arzelà)): if is compact is compact. 𝒳 {f ∈ LipL ( 𝒳 ), f(0) = 0} Corrolary : if is Lipschitz, dual solutions exists. c