Complete doubling quasiconvex metric measure spaces that are A∞ on curves admit quantitative Alberti representations μ_B = f_B dν_B with ||f_B||_L^p(ν_B) bounded independently of B for some p>1.
Subsets of rectifiable curves in Hilbert s pace—the analyst’s TSP
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Quantitative Alberti representations in spaces of bounded geometry
Complete doubling quasiconvex metric measure spaces that are A∞ on curves admit quantitative Alberti representations μ_B = f_B dν_B with ||f_B||_L^p(ν_B) bounded independently of B for some p>1.