The dimension of Cartesian product sets
- 1 April 1954
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 50 (2), 198-202
- https://doi.org/10.1017/s0305004100029236
Abstract
Given a plane set E, we denote by Ex the set of its points whose abscissae are equal to x.Throughout this paper we use the letters A and B to denote subsets of the x-axis and y-axis respectively, and we denote by A × B their Cartesian product set. We use the letters s and t to denote positive numbers; we denote by ΛsE the outer Hausdorff s-dimensional measure of the set E.This publication has 6 references indexed in Scilit:
- A correction to a paper on the dimension of Cartesian product setsMathematical Proceedings of the Cambridge Philosophical Society, 1953
- Subsets of finite measure in analytic setsIndagationes Mathematicae, 1952
- On existence of subsets of finite measure of sets of infinite measureIndagationes Mathematicae, 1952
- The Besicovitch dimension of Cartesian product setsMathematical Proceedings of the Cambridge Philosophical Society, 1950
- On Plane Sets of Fractional DimensionsProceedings of the London Mathematical Society, 1949
- The Measure of Product and Cylinder SetsJournal of the London Mathematical Society, 1945