Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
MATHEMATICA
Vol. 52, No. 2, pp. 125-130 (1995)

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On Subspaces of Measurable Real Functions

László Zsilinszky

College of Education, Department of Mathematics,
Farská 19, 949 74 Nitra - SLOVAKIA

Abstract: Let $(X,S,\mu)$ be a measure space. Let $\Phi:\Ri\to\Ri$ be a continuous function. Topological properties of the space of all measurable real functions $f$ such that $\Phi\circ f$ is Lebesgue-integrable are investigated in the space of measurable real functions endowed with the topology of convergence in measure.

Keywords: Convergence in measure; Baire category; $L_p$ spaces.

Classification (MSC2000): 28A20, 54E52

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Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.

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