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We investigate Baire-one functions whose graph is contained in the graph of a usco mapping. We prove in particular that such a function defined on a metric space with values in is the pointwise limit of a sequence of continuous functions with graphs contained in the graph of a common usco map.
We prove that any Baire-one usco-bounded function from a metric space to a closed convex subset of a Banach space is the pointwise limit of a usco-bounded sequence of continuous functions.
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