We define symmetric continuity for functions defined
on arbitrary subsets of **R**. The main result is that
when a symmetrically continuous function is defined on a
measurable set (a set with the Baire property)
then it is continuous almost everywhere (on a residual set, respectively).
This generalizes the known result for functions defined
on the whole real line.

**LaTeX 2e source
file**.
**Requires rae.cls
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**Last modified November 28, 2000.**