The space of currents arising from rectifiable sets by integrating a differential form is called the space of 2-D rectifiable currents. For a closed bounded rectifiable curve of a number of components in , bounds a rectifiable current of least Area. The theory of rectifiable currents generalizes to -D surfaces in .
See also Integral Current, Regularity Theorem
Morgan, F. ``What is a Surface?'' Amer. Math. Monthly 103, 369-376, 1996.