Remark on the theorem of Egoroff
The paper offers a generalization of Kalton-Roberts' theorem on uniformly exhaustive Maharam's submeasures to the case of arbitrary sequentially continuous functionals. Applying the result one can reduce the problem of measurability of sequential cardinals to the question whether sequentially continuous functionals are uniformly exhaustive.
In this paper we consider some spaces of differentiable multifunctions, in particular the generalized Orlicz-Sobolev spaces of multifunctions, we study completeness of them, and give some theorems.
We prove a generalised tightness theorem for cocycles over an ergodic probability preserving transformation with values in Polish topological groups. We also show that subsequence tightness of cocycles over a mixing probability preserving transformation implies tightness. An example shows that this latter result may fail for cocycles over a mildly mixing probability preserving transformation.