BANACH MANIFOLDS WITH BOUNDED STRUCTURE AND THE GAUSS-OSTROGRADSKII FORMULA

Various versions of generalization of the classical Gauss-Ostrogradskii formula to infinite-dimensional linear spaces and configuration spaces are considered in [1-7]. In the present paper, we propose a version of the Gauss-Ostrogradskii formula for Banach manifolds equipped with atlases of a special class. As far as the author knows, the obtained result is new both in the case of Banach spaces and in the case of finite-dimensional manifolds with arbitrary Borel measure. The proposed paper is an essentially improved version of the work [8].