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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],
  • {Fn}n is an UAC sequence on P,
  • g:P → R  is finite a.e. such that {(Fn)'ap}converges to g in measure, 
  • {Fn}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.