A Centroid for Sections of a Cube in a Function Space, with application to Colorimetry

The definition of the centroid in finite dimensions does not apply in a function space because of the lack of a translation invariant measure. Another approach, suggested by Nik Weaver, is to use a suitable collection of finite-dimensional subspaces. For a specific collection of subspaces of $L^1[0,1]$, this approach is shown to be successful when the subset is the intersection of a cube with a closed affine subspace of finite codimension. The techniques used are the classical Laplace Transform and saddlepoint method for asymptotics. Applications to spectral reflectance estimation in colorimetry are presented.