Chebyshev subspaces of Dirichlet series

A. Haar and A. N. Kolmogorov found necessary and sufficient conditions under which finite-dimensional subspaces in the space of continuous functions on an arbitrary compact set are Chebyshev. In this paper, we prove that subspaces of Dirichlet series in the space of $C(0, \infty ]$ of continuous and bounded functions in the interval $(0, \infty )$ that have a limit at infinity form Chebyshev subspaces.