B Lab certification is not needed to obtain Benefit corporation status. Legislation for the passage of this corporate legal status has been passed in 30 states, including Delaware, whereas B Lab Certification is privately issued by an organisation run by people principally issued from the business community.
additivity is too strong; for example, it would imply that if the measure of a set. consisting of a single point is zero, then the measure of every subset of Rn would. be zero. It is not possible to deï¬ne the Lebesgue measure of all subsets of Rn in a. geometrically reasonable way. Hausdorï¬ (1914) showed that for any dimension. n â¥ 1, there is no countably additive measure deï¬ned on all subsets of Rn that is. invariant under isometries (translations and rotations) and assigns measure one to.
Given two distinct points in V, there is a unique line containing them. Proof. Let x = y be distinct points in V, and let L 0 be the 1-dimensional vector subspace spanned by the nonzero vector y-x. Then L = x + L 0 is a line containing x and y.Suppose now that M is an arbitrary line containing x and y.Write M = z + W where dim W = 1. Then Theorem I.4 and x M = z + W imply that M = x + W.iven two distinct points in V, there is a unique line containing them. Proof. Let x = y be distinct points in V, and let L 0 be the 1-dimensional vector subspace spanned by the nonzero vector y-x. Then L = x + L 0 is a line containing x and y.