Differential Geometry on a Precise Gaussian Probability Space

Abstract

Regular disintegration corresponding to a non-degenerate functional; principle of descent — Partial function associated to a splitting — Finite codimensional projection of a slim set is slim — Implicit function theorem in finite codimension — Differential forms of degree p — Non-normalized conditional expectation of differential forms — Currents; currents along a fibre of a non-degenerate map — Submanifolds; their defining functions — Gauss map of a submanifold, its approximate continuity — Hausdorff area measure of a submanifold — Functional characterization of the area measure — Coarea formula along a non-degenerate map — The operator δ; its commutation with the non-normalized conditional expectation — Oriented submanifold — Stokes’ theorem.