Measure for families of hyperplanes systems in the affine space

Abstract

We study the problem of the measurability of families of k-hyperplanes having a common fixed point and placed in A²ⁿ⁺¹, with n ≥ 3. We prove that for k = 2n or k = 3 and 2n = 3t, for some t ∈ N, the family is not measurable.