Article 45

A Note on the convergence of UAC sequences

An. St. Univ. Ovidius Constanta 6 (1998), no. 2, 37-42.

Mathematical reviews subject classification: 26A24.

Abstract

In this paper the author proves some results on the convergence of UAC sequences of functions.

The final theorem asserts that:

If

• P is a closed subset of [a,b],
• {F_n}_n is an UAC sequence on P,
• g:P → R  is finite a.e. such that {(F_n)'_ap}_n  converges to g in measure, 
• {F_n}n converges to F on P,

then there exists G:[a,b] → R, G absolutely continuous such that G_/P = F and G'(x) = g(x) a.e. on P.