The analog of Fubini's theorem is as follows. As before, and are two orientable manifolds of pure dimensions and , and is a surjective submersion. Fix orientations of and , and give each fiber of the induced orientation. Let be an -form on , and let be an -form on that is almost everywhere positive with respect to the orientation of . Then, for almost every , the form is a well-defined integrable form on . Moreover, there is an integrable -form on defined by