A. S. Sadullaev, S. A. Imomkulov, K. Kh. Rakhimov, “Bounded Subharmonic Functions Possess the Lebesgue Property at Each Point”, Mat. Zametki, 2014, Volume 96, Issue 6,Pages <nobr>921

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Bounded Subharmonic Functions Possess the Lebesgue Property at Each Point

A. S. Sadullaev^a, S. A. Imomkulov^b, K. Kh. Rakhimov^a

^a National University of Uzbekistan named after M. Ulugbek, Tashkent
^b Navoi State Pedagogical Institute

Abstract: It is proved that the restriction of a bounded subharmonic function in a domain $D\subset\nobreak \mathbb C$ to any real line $l\subset\mathbb C$ possesses the Lebesgue property at each point of $l\cap D$.

Keywords: subharmonic function, Lebesgue property, Lebesgue point, thin set, thin point, Borel set, Diophantine number, logarithmic capacity.

UDC: 517.518.1+517.574

Received: 26.10.2013
Revised: 04.03.2013

DOI: 10.4213/mzm10377