‎Let $M(X‎, ‎mathcal{A}‎, ‎mu)$ be the ring of real-valued measurable functions‎ ‎on a measure space $(X‎, ‎mathcal{A}‎, ‎mu)$‎. ‎In this paper‎, ‎we characterize the maximal ideals in the rings of real measurable functions‎ ‎and as a consequence‎, ‎we determine when $M(X‎, ‎mathcal{A}‎, ‎mu)$ is a hereditary ring.

Motivated by the recent results on topology determined by the Sugeno and Choquet integrals we study the topology on the space of measurable functions for a non-additive measure, which is determined by the integral IS based on a semicopula S. We define a family of mappings ρS on the set of measurable functions parameterized by a semicopula S and study their properties. We show that for a semicop...

The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...

A bounded function φ : G → C on an LCA group G is called Hartman measurable if it can be extended to a Riemann integrable function φ∗ : X → C on some group compactification (ιX , X), i.e. on a compact group X such that ιX : G → X is a continuous homomorphism with image ιX(G) dense in X and φ = φ ∗ ◦ ιX . The concept of Hartman measurability of functions is a generalization of Hartman measurabil...

1. Introduction. Invariant means on spaces of functions have been studied by von Neumann [ 7], Banach [ 2], Day [ 4], [5] and others. Day's Amenable semigroups [5] presents a comprehensive summary of the earlier work and many new results. Let 2 be an abstract group or semigroup and ret (2) the Banach space of all bounded real-valued functions on 2 with the supremum norm. A mean on rei(2) is a p...