In this paper, we characterize spaces of L∞-functions on a compact Hausdorff space that are invariant under transitive and continuous group action. This work is analogous to established results concerning measurable functions space. The case for cannot be proved in the same way when endowed with norm-topology, but similar argument can used given weak*-topology, as show paper.

A function F : R2 → R is called sup-measurable if Ff : R → R given by Ff (x) = F (x, f(x)), x ∈ R, is measurable for each measurable function f : R → R. It is known that under different set theoretical assumptions, including CH, there are sup-measurable non-measurable functions, as well as their category analogues. In this paper we will show that the existence of the category analogues of supme...

In their 1976 paper, Nagel and Rudin characterize the closed unitarily Möbius invariant spaces of continuous $$L^p$$ -functions on a sphere, for $$1\le p<\infty $$ . this paper we provide an analogous characterization weak*-closed $$L^\infty sphere. We also investigate algebras

The article is an extensive review in the theory of symmetric spaces measurable functions. It contains a number new (recent) and old (known) results this field. For most results, we give their proofs or exact references, where they can be found. under consideration are Banach (or quasi-Banach) latices functions equipped with (rearrangement invariant) norm quasinorm). We consider E = E(Ω, ℱμ, μ)...