Baire class $1$ selectors for upper semicontinuous set-valued maps
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- by V. V. Srivatsa PDF
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Abstract:
Let $T$ be a metric space and $X$ a Banach space. Let $F:T \to X$ be a set-valued map assuming arbitrary values and satisfying the upper semicontinuity condition: $\{ t \in T:F(t) \cap C \ne \emptyset \}$ is closed for each weakly closed set $C$ in $X$. Then there is a sequence of norm-continuous functions converging pointwise (in the norm) to a selection for $F$. We prove a statement of similar precision and generality when $X$ is a metric space.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 337 (1993), 609-624
- MSC: Primary 54C60; Secondary 47H04, 49J45, 54C65
- DOI: https://doi.org/10.1090/S0002-9947-1993-1140919-0
- MathSciNet review: 1140919