Extensions of l. s. c. mappings into reflexive Banach spaces (Q1602978)

The author proves the following. Theorem: Let \(X\) be a collectionwise normal and countably paracompact space, \(Y\) be a reflexive Banach space, and \(\varphi:X\to 2^Y\) be a lower semi-continuous closed and convex valued mapping. Then there exists a lower semi-continuous closed and convex extension \(\varphi:\mu (X)\to 2^Y\) of \(\varphi\) over the Dieudonné completion \(\mu(X)\) of \(X\). The author also gives two generalizations.