Geodesic
Inclusions for Classes of Lacunary Sets
Canadian journal of mathematics, Tome 40 (1988) no. 2, pp. 459-476

Voir la notice de l'article provenant de la source Cambridge University Press

A sequence, a 1 < a 2 < a 3 < ..., of positive integers is called lacunary if the difference sequence dn = a n+l — an tends to infinity as n → ∞.In several recent papers we have made use of these sequences in analysis and combinatorics. In [6] we show that the class of all sets which are either finite or the range of a lacunary sequence is “full” in the sense that if (tk) is a real sequence and for each then (tk ) is an l1 sequence, that is, In [3] the class of all finite unions of sets of is shown to consist of exactly those sets of integers, A, whose characteristic sequence, χA , is in the well known summability space bs + c 0. More recently, in [1], we study lacunary sequences in connection with the conjecture of P. 
Chun, C. S.; Freedman, A. R. Inclusions for Classes of Lacunary Sets. Canadian journal of mathematics, Tome 40 (1988) no. 2, pp. 459-476. doi: 10.4153/CJM-1988-018-2
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