We prove that the assertion “For every metric space (X, d ) with a Borel measure μ such that the measure of every open ball is positive and finite, (X, d ) is separable.” lies strictly between the axiom of choice for countable collections of finite sets and the axiom of choice for countable collections of sets in deductive strength in set theory without the axiom of choice. This gives an answer to a question of Dybowski and Gorka [1].