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Covering theorems for uniqueness and extended uniqueness sets. (English) Zbl 0753.28002
A theorem that asserts that every set in a certain given class $$\mathcal C$$ can be covered by a countable union of sets in another class is called a covering theorem. Sometimes it gives the possibility of characterizing the sets of the class $$\mathcal C$$.
The present paper is devoted to prove several such theorems in the usual context of harmonic analysis wherein several previous results are already known. Full proofs are given and they are new in the case of known theorems.

##### MSC:
 28A05 Classes of sets (Borel fields, $$\sigma$$-rings, etc.), measurable sets, Suslin sets, analytic sets 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
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