Inserted: 16 nov 2007
Last Updated: 11 oct 2010
Journal: J. Math. Sciences (N.Y.)
It is proven that every real flat chain $T$ of finite mass in a metric space $E$, the density character of which is Ulam number (in particular, in a separable metric space), is rectifiable when $*M*^\alpha(T)<+\infty$ for some $\alpha\in [0,1)$, where $*M*^\alpha(T)$ stands for the $\alpha$-mass of $T$.