Skip to main content Accessibility help

The dimension of Cartesian product sets

  • J. M. Marstrand (a1)

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.

Hide All
(1)Besicovitch, A. S.On existence of subsets of finite measure of sets of infinite measure. Indag. math. 14 (1952), 339–44.
(2)Besicovitch, A. S. and Moran, P. A. P.The measure of product and cylinder sets. J. Lond. math. Soc. 20 (1945), 110–20.
(3)Davies, R. O.Subsets of finite measure in analytic sets. Indag. math. 14 (1952), 488–9.
(4)Eggleston, H. G.The Besicovitch dimension of cartesian product sets. Proc. Camb. phil. Soc. 46 (1950), 383–6.
(5)Eggleston, H. G.A correction to a paper on the dimension of cartesian product sets. Proc. Camb. phil. Soc. 49 (1953), 437–40.
(6)Moran, P. A. P.On plane sets of fractional dimensions. Proc. Lond. math. Soc. 51 (1949), 415–23.
(7)Saks, S.Theory of the Integral (Warsaw, 1937).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed