Corollary 5

— Let F, G, H be three topological vector spaces, and let (u, v) \to [u \cdot v] be a continuous bilinear mapping of F \times G into H. If f is a measurable mapping of X into F, and g is a measurable mapping of X into G, then [f \cdot g] is a measurable mapping of X into H.

In particular, if f is a measurable mapping of X into a real (resp. complex) normed space F, and g is a measurable mapping of X into R (resp. C), then gf is measurable. If F is a normed algebra and f, g are two measurable mappings of X into F, then fg is measurable.