Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-19T17:30:03.014Z Has data issue: false hasContentIssue false
  • English
  • Français

On Frequencies and Semicontinuous Functions

Published online by Cambridge University Press:  20 November 2018

F. W. Levi
F. W. Levi*
Affiliation:
Tata Institute of Fundamental Research, Bombay
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper deals with a particular class of distributive properties which appear to be important for Analysis and which I call frequencies. They can be defined for any kind of sets but it essential for proper application that a condition L (the statement of Lindelöf's lemma) is satisfied. From this condition follows Theorem 1, which is characteristic for frequencies but does not hold for other distributive properties. For every frequency F of a space Σ, one can build up an Analysis mod F of Σ the classical case is the Analysis mod F0. It is convenient to introduce the words “nearly every” with such a meaning that “every” and “almost every” are the special cases which, when we use the notation of this paper, correspond to F = F0 and F = FC.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 2 , 1950 , pp. 32 - 43
Copyright
Copyright © Canadian Mathematical Society 1950

References

[1] Caratheodory, C., Vorlesungen über reelle Funktionen (B. G. Teubner, 1919).Google Scholar
[2] Levi, F. W., On the Fundamentals of Analysis (Calcutta, 1939).Google Scholar
[3] Morse, A. P. and Randolph, J. F., “Gillespie Measure,” Duke Math. J., vol.6, pp. 408–419.Google Scholar
[4] Zoretti-Rosenthal, , “Die Punktmengen,” Encyklopadie der mathematischen Wissenschaften, II C9a.Google Scholar