T. S. S. R. K. Rao, "Proximinal subspaces of of finite codimension", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 417904, 5 pages, 2003. https://doi.org/10.1155/S0161171203212308
Proximinal subspaces of of finite codimension
We study an analogue of Garkavi's result on proximinal subspaces of of finite codimension in the context of the space of affine continuous functions on a compact convex set . We give an example to show that a simple-minded analogue of Garkavi's result fails for these spaces. When is a metrizable Choquet simplex, we give a necessary and sufficient condition for a boundary measure to attain its norm on . We also exhibit proximinal subspaces of finite codimension of when the measures are supported on a compact subset of the extreme boundary.
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