Strong measurability has a number of different meanings, some of which are explained below.
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Values in Banach spaces
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
Semi-groups
A semigroup of linear operators can be strongly measurable yet not strongly continuous. It is uniformly measurable if and only if it is uniformly continuous, i.e., if and only if its generator is bounded.