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Vitali systems of neighbouring type. (English) Zbl 0702.28002

From the author’s summary: “A generalized Vitali theorem is proved for so-called neighbouring Vitali systems consisting of cubes. A neighbouring Vitali system is characterized by the property that inside each cube one can find two separated, fairly large sets (both properties to be defined by means of the geometry and the Lebesgue measure in the following) from the Vitali system. The proof uses a bootstrap method, which cannot be applied in the simpler pointwise case.”
Reviewer: D.Plachky

MSC:

28A35 Measures and integrals in product spaces
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