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