Finite dimensional chebyshev subspaces of spaces of discontinuous functions

In this paper the author studies the existence and the characterization of the n dimensional Chebyshev subspaces of L1[a, b], B[a, b] and some other spaces of discontinuous functions. In the case when the space admits an n dimensional Chebyshev subspace, the author develops a complete characterization for those n dimensional Chebyshev subspaces. In the case when the space does not admit an n dimensional Chebyshev subspaces, the author proves it.