A Remark on a Theorem of Losert.
A remark on a theorem of Solecki
S. Solecki proved that if is a system of closed subsets of a complete separable metric space , then each Suslin set which cannot be covered by countably many members of contains a set which cannot be covered by countably many members of . We show that the assumption of separability of cannot be removed from this theorem. On the other hand it can be removed under an extra assumption that the -ideal generated by is locally determined. Using Solecki’s arguments, our result can be used...
A remark on Edgar's extremal integral representation theorem
A remark on Slutsky's theorem
A remark on the existence of the ergodic Hilbert transform
A remark on the uniformization in metric ѕpaces
A remark on the weighted averages for superadditive processes.
A remark on weak McShane integral
We characterize the weak McShane integrability of a vector-valued function on a finite Radon measure space by means of only finite McShane partitions. We also obtain a similar characterization for the Fremlin generalized McShane integral.
A Renewal Approach to the Perron-Frobenius Theory of Non-negative Kernels on General State Spaces.
A representation theorem for
A representation theorem for compact-valued multifunctions
A representation theorem for operators on a space of interval functions.
A representation theorem for perfect partitions of -actions with finite entropy
A representation theorem for the second dual of C[0,1]
A representation theorem for time-scale functionals
A result of J. Bourgain: has the Dunford-Pettis property
A reverse maximal ergodic theorem
A Riemann approach to random variation
This essay outlines a generalized Riemann approach to the analysis of random variation and illustrates it by a construction of Brownian motion in a new and simple manner.
A Riesz representation theory for completely regular Hausdorff spaces and its applications
Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let Cb(X, E) be the space of all E-valued bounded, continuous functions on X, equipped with the strict topology β. We develop the Riemman-Stieltjes-type Integral representation theory of (β, || · ||F) -continuous operators T : Cb(X, E) → F with respect to the representing Borel operator measures. For X being a k-space, we characterize strongly bounded (β, || · ||F)-continuous operators T : Cb(X, E) → F. As an application, we...
A rough curvature-dimension condition for metric measure spaces
We introduce and study a rough (approximate) curvature-dimension condition for metric measure spaces, applicable especially in the framework of discrete spaces and graphs. This condition extends the one introduced by Karl-Theodor Sturm, in his 2006 article On the geometry of metric measure spaces II, to a larger class of (possibly non-geodesic) metric measure spaces. The rough curvature-dimension condition is stable under an appropriate notion of convergence, and stable under discretizations as...