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Sep 17, 2013 at 10:53 comment added Pietro Majer Since the other direction is a consequence of the metrizability of the space of real-valued measurable functions on $(X,\mathcal{A},\mu)$, one may look for whom introduced a distance on that space (Frechét?).
Sep 17, 2013 at 9:43 history answered Michael Greinecker CC BY-SA 3.0