Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-25T04:36:57.577Z Has data issue: false hasContentIssue false
  • English
  • Français

On some series of functions

Published online by Cambridge University Press:  24 October 2008

R. E. A. C. Paley
R. E. A. C. Paley
Affiliation:
Trinity College
Get access Rights & Permissions [Opens in a new window]

Extract

We now consider some properties of “almost all” series

where the numbers vary independently in the interval (0, 1). What we need is a definition of measure in the space of sequences or, what is the same thing, in the space

of infinitely many dimensions. Such a definition has been given by Steinhaus. He defines a correspondence between the cube (7.2) and the interval (0,1) in the following way:

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 26 , Issue 4 , October 1930 , pp. 458 - 474
Copyright
Copyright © Cambridge Philosophical Society 1930

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Jessen, B., 1. Bidrag til integralteorien for funktioner of uendelig mange variable (1930).Google Scholar
Khintchine, A., 1. “Über dyadische Brüche”, Math. Zeitschrift, XVIII (1923), 109–116.CrossRefGoogle Scholar
Khintchine, A., 2. “Über einen Satz der Wahrscheinlichkeitsrechnung”, Fundamenta Math., VI (1924), 9–20.CrossRefGoogle Scholar
Steinhaus, H., 1. “Über die Wahrscheinlichkeit dafür, daß der Konvergenzkreis einer Potenzreihe ihre natürliche Grenze ist”, Math. Zeitschrift, XXI (1929), 408–416.Google Scholar
Steinhaus, H.,2. “Sur la probabilité de la convergence de séries”, Studia Math., II (1930), 21–39.CrossRefGoogle Scholar
Töplitz, O., 1. “Über allgemeine lineare Mittelbildungen”, Prace Matematyczno-Fizyczne, XXII (1911), 113–119.Google Scholar
Zygmund, A., 1. “Sur les séries trigonométriques lacunaires”, Journal London Math. Soc. V (1930), 138–145.CrossRefGoogle Scholar
Zygmund, A., 2. “On the convergence of lacunary trigonometric series”, Fundamenta Math., XVI (1930), 90–107.CrossRefGoogle Scholar