Geodesic
On Measures Determined by Continuous Functions that are not of Bounded Variation
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 121-124

Voir la notice de l'article provenant de la source Cambridge University Press

In [1] it was shown that a continuous function of bounded variation on the real line determined a Method II outer measure for which the Borel sets were measurable and the measure of an open interval was equal to the total variation of f over the interval. The monotone property of measures implied that if an open interval I on which f was not of bounded variation contained subintervals on which f was of finite but arbitrarily large total variation then the measure of I was infinite. Since there are continuous functions that are not of bounded variation over any interval (e.g. the Weierstrasse nondifferentiable function) the general case was not resolved. 
Burry, J. H. W.; Ellis, H. W. On Measures Determined by Continuous Functions that are not of Bounded Variation. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 121-124. doi: 10.4153/CMB-1970-025-0
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[1] 1. Ellis, H. W. and Jeffery, R. L., On measures determined by functions with finite right and left limits everywhere. Canad. Math. Bull. (2) 10 (1967), 207-225. Google Scholar

[2] 2. Munroe, M. E., Introduction to measure and integration, Addison-Wesley, Cambridge, Mass. 1953. Google Scholar

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