Abstract
This chapter discusses the radon transform and generalized functions on a real affine space. It describes the integrals over a hyperplane and presents a scenario involving an n-dimensional real affine space consisting of points x = (x1,…,xn). The space is assumed to be oriented. The differential form dx = dx1…dxn is assumed to be a volume element in this space. It discusses a fundamental difference between inversion formulas for odd and even dimensions. In the case of odd dimension, the inversion formula is local in that the value of a function f at some point x depends only on the integrals of f over hyperplanes passing through x and over hyperplanes infinitesimally close to these.
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