The fractional dimensional theory of continued fractions
- 1 July 1941
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 37 (3) , 199-228
- https://doi.org/10.1017/s030500410002171x
Abstract
The notion of fractional dimensions is one which is now well known. The object of the present paper is the investigation of the dimensional numbers of sets of points which, when expressed as continued fractions, obey some simple restriction as to their partial quotients. The sets considered are naturally of linear measure zero. Those properties of the partial quotients which hold for almost all continued fractions make up the subject called by Khintchine ‘the measure theory of continued fractions’.Keywords
This publication has 1 reference indexed in Scilit:
- Sets of Fractional Dimensions (IV): On Rational Approximation to Real NumbersJournal of the London Mathematical Society, 1934