Embedding function spaces into

We show that if the space ℓ ∞ / c 0 contains an isometric copy of every function space over a first countable compactum or every function space over a Corson compactum of weight not exceeding the continuum then every subset of R 2 belongs to the σ-field generated by sets of the form A 1 × A 2 . We prove a similar result about isomorphic rather than isometric embeddings into ℓ ∞ / c 0 in terms of the σ-field of subsets of R k generated by sets of the form A 1 × ⋯ × A k for other positive integers k.