PORTUGALIAE MATHEMATICA Vol. 52, No. 2, pp. 125130 (1995) 

On Subspaces of Measurable Real FunctionsLászló ZsilinszkyCollege 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 Lebesgueintegrable 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 Full text of the article:
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