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Multiplicativity of the uniform norm and independent functions

Published online by Cambridge University Press:  17 April 2009

A. Guyan Robertson
A. Guyan Robertson
Affiliation:
University of Edinburgh, Department of Mathematics King's Buildings Mayfield Road Edinburgh EH9 3JZ, Scotland
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It has long been known that there is a close connection between stochastic independence of continuous functions on an interval and space-filling curves [9]. In fact any two nonconstant continuous functions on [0, 1] which are independent relative to Lebesgue measure are the coordinate functions of a space filling curve. (The results of Steinhaus [9] have apparently been overlooked in more recent work in this area [3, 5, 6].)

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 1 , August 1990 , pp. 153 - 155
Copyright
Copyright © Australian Mathematical Society 1990

References

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