Integration of differential forms on manifolds with locally finite variations. Part II

In the part I of the paper the $n$-dimensional $C^0$-manifolds in $\mathbb R^n$ $(m\ge n)$ with locally finite $n$-dimensional variations (a generalization of locally rectifiable curves to dimension $n>1$) and integration of measurable differential $n$-forms over such manifolds were defined. The main result of part II states that an $n$-dimensional manifold $C^1$-embedded in $\mathbb R^m$ has locally finite variations and the integral of measurable differential $n$-form defined in part I can be calculated by well-known formula.