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Article 15

Monotonicity and local systems

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

Mathematical reviews subject classification: 26A48.



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 (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.