# Monotonicity and local systems

### Real Analysis Exchange 17 (1991/92), 291-313.

#### Mathematical reviews subject classification: 26A48.

## Abstract

Using the notion of a local system with some *intersection** conditions*, considered by Thomson in *Real functions* (Lecture Notes in Mathematics, 1170, Springer-Verlag 1985) and in *Derivation bases on the real line* (I and II, Real Analysis Exchange **8 **(1982/3), 67-208, 280-442), we extend Theorems 6, 3 and 4 of Preiss (*Approximate derivatives and Baire classes,* Czech. Math. J., **21 **(96), (1971), 373-382).

The main result of this paper is the monotonicity Theorem 4.

In Article 7 the author extends Bruckner's reduction Theorem (see Theorem 8), but we don't know if Theorem 4 of Preiss and our Theorem 4 follow by Theorem 8 of Article 7.