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**Strong measurability** has a number of different meanings, some of which are explained below.

For a function *f* with values in a Banach space (or Fréchet space), *strong measurability* usually means Bochner measurability.

However, if the values of *f* lie in the space of continuous linear operators from *X* to *Y*, then often *strong measurability* means that the operator *f(x)* is Bochner measurable for each fixed *x* in the domain of *f*, whereas the Bochner measurability of *f* is called *uniform measurability* (cf. "uniformly continuous" vs. "strongly continuous").

A family of bounded linear operators combined with the direct integral is strongly measurable, when each of the individual operators is strongly measurable.

A semigroup of linear operators can be strongly measurable yet not strongly continuous.^{[1]} It is uniformly measurable if and only if it is uniformly continuous, i.e., if and only if its generator is bounded.