Published online by Cambridge University Press: 24 October 2008
The Pompeiu problem has its origins in classical analysis in ℝn (see [2, 3, 4, 8] for a discussion and some history). In this context it may be stated as follows. Let D ⊂ ℝn be a bounded measurable set of positive Lebesgue measure and f a locally integrable function on ℝn. Then, if ∫σ(D)f = 0 for all rigid motions σ of ℝn, is f = 0?