*Published Paper*

**Inserted:** 16 nov 2007

**Last Updated:** 11 oct 2010

**Journal:** J. Math. Sciences (N.Y.)

**Volume:** 167

**Number:** 3

**Pages:** 406-417

**Year:** 2010

**Notes:**

(preprint 2007)

**Abstract:**

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 $T$.

**Keywords:**
flat chain, fractional mass, $\alpha$-mass, metric current

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