University of Qom Measure Algebras and Applications 3116-014X 1 1 2023 09 23 Some notes about Orlicz spaces related to a Banach function space نکاتی در مورد فضاهای اورلیش مرتبط با یک فضای باناخ تابعی 74 82 2520 10.22091/maa.2023.9422.1001 EN AliReza Bagheri Salec Department of Mathematics, University of Qom, Qom, Iran 0000-0002-4917-6125 Journal Article 2023 05 10  Orlicz spaces, as a very important generalization of Lebesgue spaces, were proposed more than 100 years ago and were first introduced by Z. W. Birnbaum and W. Orlicz. َAfter that, another generalization of Lebesgue spaces with symbols X^p instead of L^p was introduced in which X is a Banach function space. In this article, another generalization of Lebesgue spaces is investigated, which includes both previous generalizations. Although this generalization and preliminary studies of it were published in a scientific report in 1988, effective research on this generalization was done 15 years ago. Due to the fact that in this generalization a convex and Young function Φ is placed instead of function |.|^p and a Banach function space X is placed instead of space L^1, in this article, taking into account the conditions of the function Φ we will check properties of generalized Orlicz space X^Φ. https://maa.qom.ac.ir/article_2520_c6a19636a6a173eeb1efef3041789221.pdf