Chen, Shutao On vector valued Orlicz spaces. (English) Zbl 0531.46022 Chin. Ann. Math., Ser. B 5, 293-304 (1984). In the paper [M. S. Skaff, Pac. J. Math. 28, 413-430 (1969; Zbl 0176.110)], two main results are stated as follows:(1) The Orlicz class \(L_ M\) is a vector space iff M(t,x) satisfies a \(\Delta\)-condition;(2) If mes T\(<\infty\), then modular convergence and norm convergence in Orlicz space \(L_ M\) are equivalent iff M(t,x) satisfies a \(\Delta\)- condition.In this article, the author gives a counterexample to show the incorrectness of proofs of those two results, and shows that the results still hold even without the restriction mes T\(<\infty\). MSC: 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Keywords:modular convergence; norm convergence in Orlicz space Citations:Zbl 0176.110 PDFBibTeX XMLCite \textit{S. Chen}, Chin. Ann. Math., Ser. B 5, 293--304 (1984; Zbl 0531.46022)