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Article 12

Semicontinuity conditions and monotonicity

Real Analysis Exchange 14 (1989), 293-413.

Mathematical reviews subject classification: 26A48.

 


Abstract

In Article 8 we proved a theorem (Theorem 8) which extends Bruckner's reduction theorem.

But this theorem cannot be applied to lower internal functions in Baire class one.
         
In our paper we give another extension of Bruckner's theorem and of our theorem of Article 7, which can also be applied to the above mentioned class of functions.

For this purpose we introduce some conditions of Darboux type, and so we find some equivalent definitions for the lower internal functions in Baire class one.

The lower internal functions were introduced by Garg in A new notion of derivative (Real Analysis Exchange 7 (1981/2), 65-84), and it is that paper which initially stimulated this research.