N. E. Gretsky and J. J. Uhl, Jr. Representations of bounded linear operators on Banach function spaces of vector-valued functions to Banach spaces are given in terms of operator-valued measures. Then ...
Let $X$ and $Y$ be metric spaces and $f: X \rightarrow Y$ a Borel measurable function. Does $f$ have to be of bounded class, i.e. are the sets $f^{-1}\lbrack H ...