The Egoroff theorem for non-additive measures in Riesz spaces
The Egoroff theorem remains valid for any Riesz space-valued non-additive measure which is continuous from above and below by assuming that the Riesz space has the asymptotic Egoroff property. This property is satisfied for many concrete Riesz spaces, such as R-S of all real functions on a non-empty set S, L-0[0, 1] of all Lebesgue measurable functions, and their ideals. (C) 2006 Elsevier B.V. All rights reserved.
non-additive measures riesz space the asymptotic egoroff property the egoroff condition