Open Access
1997/1998 Intersection Properties of Directional Essential Cluster Sets
A. K. Layek
Author Affiliations +
Real Anal. Exchange 23(2): 757-766 (1997/1998).


Jarnik in 1936 proved a remarkable property of directional cluster sets. This result states that for a function \(f\) defined on the open upper half plane to the extended real line, each pair of directional cluster sets intersect at all points on the real line but a countable set of points. An example was constructed to show that the exact analogue of Jarnik’s result fails for directional essential cluster sets. Here we shall establish a certain variant of this analogue for directional essential cluster sets of measurable functions.


Download Citation

A. K. Layek. "Intersection Properties of Directional Essential Cluster Sets." Real Anal. Exchange 23 (2) 757 - 766, 1997/1998.


Published: 1997/1998
First available in Project Euclid: 14 May 2012

MathSciNet: MR1639961
zbMATH: 0943.30019

Primary: 30D40

Keywords: {countable} , {densities} , {directional cluster sets} , {directional essential cluster sets} , {Lebesgue outer measure}

Rights: Copyright © 1999 Michigan State University Press

Vol.23 • No. 2 • 1997/1998
Back to Top