Menger curvature and rectifiability in metric spaces
Abstract
We show that for any metric space X the condition \[ ∫X∫X∫X c(z1,z2,z3)2\, d z1\, d z2\, d z3 < ∞, \] where c(z1,z2,z3) is the Menger curvature of the triple (z1,z2,z3), guarantees that X is rectifiable.
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