An \(L_{p}\)-function determines \(\ell_{p}\). (English) Zbl 1142.26314

Summary: \(\ell_{p}\) is characterized by the convergence of a series defined by an \(L_{p}\)-function on the real line \(\mathbb{R}\).


26D10 Inequalities involving derivatives and differential and integral operators
46A45 Sequence spaces (including Köthe sequence spaces)
60G30 Continuity and singularity of induced measures
Full Text: DOI Euclid


[1] L. A. Shepp, Distinguishing a sequence of random variables from a translate of itself, Ann. Math. Statist. 36 (1965), 1107-1112. · Zbl 0136.40108
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