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In this note we extend White's deformation theorem for G-flat chains to thesetting of G-flat tensor chains. As a corollary we obtain that the groups ofnormal tensor chains identify with some subgroups of normal chains. Moreoverthe corresponding natural group isomorphisms are isometric with respect tonorms based on the coordinate slicing mass. The coordinate slicing mass of ak-chain is the integral of the mass of its 0-slices along all coordinate-planesof codimension k. The fact that this quantity is equivalent to the usual massis not straightforward. To prove it, we use the deformation theorem and apartial extension of the restriction operator defined for all chains (not onlyof finite mass). On the contrary, except in some limit or degenerate cases, thewhole groups of tensor chains and of finite mass tensor chains do not identifynaturally with subgroups of chains.

A deformation theorem for tensor flat chains and applications (complement to ''Tensor rectifiable G-flat chains'')