Authors: A. M. Vinogradov and L. Vitagliano

Basic elements of integral calculus over algebras of iterated differential forms Λ_k, k<∞, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms are computed. Various applications and the integral calculus over the algebra Λ_∞ will be discussed in subsequent notes.

To appear in Doklady Akademii Nauk (Doklady Mathematics). See also arXiv: math.DG/0610914.

6 pages, LaTeX-2e.

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