Annihilating probability measures under constraints

Abstract

Let P be a probability measure and H ⊆ L ^∞(P) be a linear subspace and 0 < c ≤ 1 ≤ C real constants. Then we give a relatively computable criterion whether or not there exists a H-annihilating probability measure Q ∼ P equivalent to P with density c ≤ dQ/dP ≤ C. In fact we also prove a version where L ^∞(P) is replaced by C(K) for a compact Hausdorff space K.