Finite Dimesional Spaces
نویسنده
چکیده
We assume that a flat space E with translation space V is given and we put n := dimE = dimV. Let B be a norming cell of V (see Vol.I, Sect.51). A concept of volume for the space E should have the following property: If the norming cell B has volume 1, then a cell in E modelled on B of a given scale s ∈ P I has volume s. (Recall that such a cell is a set of the form q + sB, with q ∈ E .) Intuitively, a subset S of E will be negligible with respect to volume if it can be covered by a finite collection of cells whose total volume can be made arbitrarily small. This is the motivation for the following:
منابع مشابه
Finite Dimesional Spaces Vol.II
Λ(A)(f) = (−1)A(u)(delp(f)) + (−1) A(u)(delq(f)). (11.5) It is clear from (11.4) and the definition (11.2) that delp(f) = del(p+1)(f). Hence the two terms on the right side of (11.5) cancel and we have Λ(A)(f) = 0. Since the non-injective f ∈ Vk+1 with adjacent repeated terms was arbitrary, it follows from Prop.9 of Sect.11 that Λ(A) is skew. In View of the Lemma, we may regard (11.3) as the de...
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