IJPAM: Volume 88, No. 4 (2013)


Kifah Y. Al-Hami
Department of Mathematics
University of Bahrain
P.O. Box 32038, Sukhair, BAHRAIN

Abstract. Consider a lebesgue measure $\lambda$ on $[0\,,\,1]$ and let $0\leq h\in L^{1}(\lambda)$. We construct a measure $\mu$ such that $\left\Vert\mu\right\Vert \leq2.\,\left\Vert h\right\Vert _{L^{1}(\lambda)}$, $\mu\bot\lambda$ and $\mu\left( E\right) =0$, for every Carleson set $E$ in $[0\,,1]$ and converges weak-star to $h\,d\lambda$.

Received: July 31, 2013

AMS Subject Classification: Carleson set, weak-star convergence, Cantor set, $L^{1}(\lambda)$

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DOI: 10.12732/ijpam.v88i4.6 How to cite this paper?
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 88
Issue: 4