## Real Analysis Exchange

### Recursive set relations.

#### Abstract

Let $A(x)$, $B(x)$, $C(x)$ be characteristic functions of three measurable sets of real numbers. We determine necessary and sufficient conditions for which $A(x+a_{n})+B(x+b_{n})+C(x+c_{n})=A(x)+B(x)+C(x)$ almost everywhere, where $\{ a_n\},\{ b_n\},\{ c_n\}$ are sequences of nonzero shifts approaching zero.

#### Article information

Source
Real Anal. Exchange Volume 29, Number 2 (2003), 835- 851.

Dates
First available in Project Euclid: 7 June 2006