Abstract: There are basically two approaches to geometric measure theory, which
grew out of the theory of minimal
surfaces. There is the De Giorgi approach via Cacciopoli sets and BV
functions and Federer´s approach
which from the start looked at generalized submanifolds of arbitrary
codimension.
We show how at least the question of rectifiability in arbitrary
codimension can be reduced to that in codimension one
and that means dealt with in the De Giorgi framework. We are also able to
define a new compactness class of rectifiable currents
generalizing Federer-Fleming. This is joint work with E. Spadaro (La
Sapienza)