A simplified conjugation scheme for lower semi-continuous functions

Computability on Continuou, Lower Semi-continuous and Upper Semi-continuous Real Functions

In this paper we investigate continuous and upper and lower semi-continuous real functions in the framework of TTE, Type-2 Theory of EEectivity. First some basic facts about TTE are summarized. For each of the function spaces, we introduce several natural representations based on diierent intiuitive concepts of \eeectivity" and prove their equivalence. Computability of several operations on the...

On the Epi - Compactness Ofequi - Lower Semi - Continuous Functions

In this paper we show that equi-lsc. functions from a topological vector space X to the extended reals are epi-compact without assuming the local compactness or the second countablity of the underlying space X. We also show that weakly equi-lower semicontinuous functions from a Banach space X to the extended reals are Mosco-compact. Finally, we apply these results to prove the Mosoc-compactness...

Convex extensions and envelopes of lower semi-continuous functions

We define a convex extension of a lower-semicontinuous function to be a convex function that is identical to the given function over a pre-specified subset of its domain. Convex extensions are not necessarily constructible or unique. We identify conditions under which a convex extension can be constructed. When multiple convex extensions exist, we characterize the tightest convex extension in a...

A Theorem on Semi-Continuous Functions

A Theorem on Semi - Continuous Functions

RECENTLY G. C. Young* and A. Denjoyf have communicated theorems—those in Denjoy's memoir are of an especially comprehensive character—dealing, in particular, with point sets where the four derivatives of a given continuous function are identical. It is the purpose of this note to treat an analogous problem that arises when "derivative" is replaced by "saltus."$ However, instead of confining our...