# A note on an assumption of P. Y. Lee and T. S. Chew

### Real Analysis Exchange 21 (1995-1996), no.2, 755-757.

#### Mathematical reviews subject classification: 26A39; 26A24.

## Abstract

The aim of this article is to prove the following assertion (see Corollary 1):

Let F:[a,b] → R and let E_{i}, i = {1,n} be closed subsets of [a,b].

Let F_{n}:[a,b] → R, such that

F_{n}(x) = F(x), for and

F_{n} is linear on the closure of each interval contiguous to.

If F is continuous on [a,b] and F ∈ AC* on each E_{i} then F_{n} is derivable a.e. on [a,b] and F'_{n} is summable on [a,b].

In *A Riesz-type definition of the Denjoy integral *(Real Analysis Exchange **11** (1985/6), p.224) P.Y. Lee and T.S. Chew use this result essentially, without proof and without stating it explicitly, claiming that "it is easy to verify''.

The same result is also used by P.Y. Lee in Theorem 10.2 of *Lanzhou lectures on Henstock integration* (World Scientific, Singapore, 1989, p. 59).