Let $fM(X)$ be the space of all finite regular Borel measures on $X$. A general measure algebra is a subspace of $fM(X)$, which is an $L$-space and has a multiplication preserving the probability measures. Let $cLsubseteqfM(X)$ be a general measure algebra on a locally compact space $X$. In this paper, we investigate the relation between Arens regularity of $cL$ and the topology of $X$. We find conditions under which the Arens regularity of $fL$ implies the compactness of $X$. We show that these conditions are necessary. We also present some examples in showing that the new conditions are different from Theorem 3.1 of cite{7}.
Laali, J. & Ettefagh, M. (2012). Non-regularity of multiplications for general measure algebras. Bulletin of the Iranian Mathematical Society, 38(1), 265-274.
MLA
Laali, J., & Ettefagh, M. "Non-regularity of multiplications for general measure algebras", Bulletin of the Iranian Mathematical Society, 38, 1, 2012, 265-274.
HARVARD
Laali J., Ettefagh M. (2012). 'Non-regularity of multiplications for general measure algebras', Bulletin of the Iranian Mathematical Society, 38(1), pp. 265-274.
CHICAGO
J. Laali & M. Ettefagh, "Non-regularity of multiplications for general measure algebras," Bulletin of the Iranian Mathematical Society, 38 1 (2012): 265-274,
VANCOUVER
Laali J., Ettefagh M. Non-regularity of multiplications for general measure algebras. BIMS. 2012;38(1):265-274.
