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Lemma 5.8 . [04EA]

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Lemma 5.8.

(Continuity of the Solomon functional) All Lagrangians are assumed to be contained in a fixed bounded region of XX, homologous to L0L_{0}, and are quantitatively almost calibrated. Suppse LiL_{i} is a sequence of Lagrangian integral currents with potential fLif_{L_{i}}, such that Li→LL_{i}\to L in the flat norm, and fLi​Lif_{L_{i}}L_{i} converge to fL​Lf_{L}L as currents, then the Solomon functionals converge: 𝒮⁡(Li)→𝒮⁡(L)\mathcal{S}(L_{i})\to\mathcal{S}(L).

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