Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  075.04701
Autor:  Erdös, Pál; Karamata, J.
Title:  Sur la majorabilité C des suites de nombres réels. (C-majorability of sequences of real numbers) (In French)
Source:  Acad. Serbe Sci., Publ. Inst. Math. 10, 37-52 (1956).
Review:  A sequence {an} of real numbers is said to be C-majorable if there is a sequence {An} such that an \leq An (n = 1,2,...) and (A1+···+An)/n tends to a finite limit. In the first part of the paper various sets of necessary and sufficient conditions are established for a sequence to be C-majorable. Thus it is shown, for example, that {an} is C-majorable if and only if, for every k = o(n), sumr = n+1n+k ar = o(n) and, for every \epsilon > 0 and m \geq (1+\epsilon) n, limsupn, n ––> oo {1 \over m-n} sumr = n+1n ar < oo. In the second part of the paper, certain Tauberian theorems and the prime number theorem are discussed in the light of the concept of C-majorability.
Reviewer:  L.Mirsky
Classif.:  * 40A99 Convergence of infinite limiting processes
Index Words:  Series

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