Two random constructions inside lacunary sets
The main result says that every polynomial sequence of integers or the sequence of primes contain a subsequence \(E\) that is a \(\Lambda (p)\)-set for all \(p<\infty\) but not a Rosenthal set (i.e., not all \(L^\infty\)-functions with spectrum in \(E\) are continuous). The proof is done by random choice.
scientific article; zbMATH DE number 1368751
scientific article