# 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.