Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213220220701On some properties of elements in hypergroup algebras33073312740110.22075/ijnaa.2021.23709.3960ENAliGhaffariDepartment of Mathematics, University of Semnan, P. O. Box 35195-363, Semnan, IranJournal Article20210204Let $H$ be a hypergroup with left Haar measure and let $L^1(H)$ be the complex Lebesgue space associated with it. Let $L^\infty(H)$ be the set of all locally measurable functions that are bounded except on a locally null set, modulo functions that are zero locally a.e. Let $\mu\in M(H)$. We want to find out when $\mu F\in L^\infty(H)^*$ implies that $F\in L^1(H)$. Some necessary and sufficient conditions is found for a measure $\mu$ for which if $\mu F\in L^1(H)$ for every $F\in L^\infty(H)^*$, then $F\in L^1(H)$.https://ijnaa.semnan.ac.ir/article_7401_120da88299bb964015cb0bdccb1b9e97.pdf