# Article

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Keywords:
$\sigma$-porosity; sets of extended uniqueness; trigonometric series; $H^{(n)}$-sets
Summary:
We show that there exists a closed non-$\sigma$-porous set of extended uniqueness. We also give a new proof of Lyons' theorem, which shows that the class of $H^{(n)}$-sets is not large in $U_0$.
References:
[BKR] Bukovský L., Kholshchevnikova N.N., Repický M.: Thin sets of harmonic analysis and infinite combinatorics. Real Analysis Exchange 20.2 (1994-95), 454-509. MR 1348075
[DSR] Debs G., Saint-Raymond J.: Ensembles boréliens d'unicité et d'unicité au sens large. Ann. Inst. Fourier (Grenoble) 37 (1987), 217-239. MR 0916281
[D] Dolzhenko E.P.: Boundary properties of arbitrary functions (in Russian). Izv. Akad. Nauk. SSSR Ser. Mat. 31 (1967), 3-14. MR 0217297
[KL] Kechris A., Louveau A.: Descriptive Set Theory and the Structure of Sets of Uniqueness. Cambridge U. Press, Cambridge (1987). MR 0953784 | Zbl 0642.42014
[L] Lyons R.: The size of some classes of thin sets. Studia Math. 86.1 (1987), 59-78. MR 0887312 | Zbl 0628.43006
[T] Tkadlec J.: Construction of a finite Borel measure with $\sigma$-porous sets as null sets. Real Analysis Exchange 12 (1986-87), 349-353. MR 0873903 | Zbl 0649.28005
[Š] Šleich P.: Sets of type $H^{(s)}$ are $\sigma$-bilaterally porous. unpublished.
[Z$_1$] Zajíček L.: Sets of $\sigma$-porosity and sets of $\sigma$-porosity(q). Časopis Pěst. Mat. 101 (1976), 350-359. MR 0457731 | Zbl 0341.30026
[Z$_2$] Zajíček L.: Porosity and $\sigma$-porosity. Real Analysis Exchange 13 (1987-88), 314-350. MR 0943561
[Z$_3$] Zajíček L.: A note on $\sigma$-porous sets. Real Analysis Exchange 17.1 (1991-92), 18.

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