A Note on a Theorem of A. D. Alexandroff
A note on almost strong liftings
Let be a locally compact space. A lifting of where is a positive measure on , is almost strong if for each bounded, continuous function , and coincide locally almost everywhere. We prove here that the set of all measures on such that there exists an almost strong lifting of is a band.
A note on almost sure convergence and convergence in measure
The present article studies the conditions under which the almost everywhere convergence and the convergence in measure coincide. An application in the statistical estimation theory is outlined as well.
A note on angular semigroups.
A note on Carathéodory type function
A note on cocycles in ergodic theory
A note on complex unions of subsets of the real line
A note on conservative measures on semigroups.
A note on convergence of level sets.
A note on counting cuspidal excursions.
A note on determinacy of measures
A note on equivalent interval covering systems for Hausdorff dimension on R.
A note on ideals of compact sets
Solecki has shown that a broad natural class of ideals of compact sets can be represented through the ideal of nowhere dense subsets of a closed subset of the hyperspace of compact sets. In this note we show that the closed subset in this representation can be taken to be closed upwards.
A note on integral representation of Feller kernels
We consider integral representations of Feller probability kernels from a Tikhonov space X into a Hausdorff space Y by continuous functions from X into Y. From the existence of such a representation for every kernel it follows that the space X has to be 0-dimensional. Moreover, both types of representations coincide in the metrizable case when in addition X is compact and Y is complete. It is also proved that the representation of a single kernel is equivalent to the existence of some non-direct...
A note on intersections of non-Haar null sets
We show that in every Polish, abelian, non-locally compact group G there exist non-Haar null sets A and B such that the set {g ∈ G; (g+A) ∩ B is non-Haar null} is empty. This answers a question posed by Christensen.
A note on Lebesgue spaces
A note on Lusin measurability in measure spaces
A note on Lusin's condition (N)
A note on measurability of trajectories of a stochastic process
A note on measurable functions