On vector valued Orlicz spaces (Q788244)

In the paper [\textit{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\(<\infty\).