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

Abstract

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.

Citation

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

Information

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

MathSciNet: MR1639961
zbMATH: 0943.30019

Subjects:
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
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