We show that every array (x(i; j) : 1 i < j < 1) of elements in a point-wise compact subset of the Baire-1 functions on a Polish space, whose iterated pointwise limit lim i lim j x(i; j) exists, is converging Ramsey-uniformly. An array (x(i; j) i<j) in a Hausdorr space T is said to converge Ramsey-uniformly to some x in T , if every subsequence of the positive integers has a further subsequence...

2Weissman, S. I., J. Chem. Phys., 29, 1189 (1958). 3 Commoner, B., J. J. Heise, B. B. Lippincott, R. E. Norberg, J. V. Passonneau, and J. Townsend, Science, 126, 57-63 (1957). 4 Sogo, P. B., N. B. Pon, and M. Calvin, these PROCEEDINGS, 43, 387-393 (1957). 5 Commoner, B., "Electron spin resonance studies of photosynthetic systems" in Light and Life, ed. W. D. McElroy and B. Glass (Baltimore: Joh...

We present an extension of the Gromov-Hausdorff metric on the set of compact metric spaces: the Gromov-Hausdorff-Prokhorov metric on the set of compact metric spaces endowed with a finite measure. We then extend it to the non-compact case by describing a metric on the set of rooted complete locally compact length spaces endowed with a locally finite measure. We prove that this space with the ex...

We describe the standard model of random walk in random environment (RWRE) on Z. Let Ω be a Polish space and S its Borel σ-algebra. Let {Tz : z ∈ Z} be a group of continuous commuting bijections on Ω: Tx+y = TxTy and T0 is the identity. Let P be a probability measure on (Ω,S) that is ergodic under this group. In other words, the σ-algebra of Borel sets invariant under {Tz} is trivial under P. D...

It is shown that a measurable function from an atomless Loeb probability space (Ω,A, P ) to a Polish space is at least continuum-to-one valued almost everywhere. It follows that there is no injective mapping h : [0, 1] → Ω such that h([a, b]) is Loeb measurable for each 0 ≤ a < b ≤ 1 and P (h([0, 1])) > 0. Thus, when an atomless Loeb measurable algebra on an internal set of cardinality continuu...

We discuss positive Miyadera–Voigt type perturbations for bi-continuous semigroups on \(\mathrm {AL}\)-spaces with an additional locally convex topology generated by additive seminorms. The main example of such spaces is the space bounded Borel measures (on a Polish space).

We present an extension of the Gromov-Hausdorff metric on the set of compact metric spaces: the Gromov-Hausdorff-Prokhorov metric on the set of compact metric spaces endowed with a finite measure. We then extend it to the non-compact case by describing a metric on the set of rooted complete locally compact length spaces endowed with a boundedly finite measure. We prove that this space with the ...

For fX i g i1 a sequence of i.i.d. random variables taking values in a Polish space with distribution , we obtain large and moderate deviation principles for the processes fn ?1 P nt] i=1 X i ; t 0g n1 and fn ?1=2 P nt] i=1 (X i ?); t 0g n1 , respectively. Given a class of bounded functions F on , we then consider the above processes as taking values in the Banach space of bounded functionals o...

This article presents the original results of Polish language statistical analysis, based on the orthographic and phonemic language corpus. Phonemic language corpus for Polish was developed by using automatic grapheme-to-phoneme conversion of the source orthographic language corpus, obtained from the National Corpus of Polish (NCP). The corpus contains the most frequently used Polish words, wri...

We show that, for the space of Borel probability measures on a Borel subset of a Polish metric space, the extreme points of the Prokhorov, Monge-Wasserstein and Kantorovich metric balls about a measure whose support has at most n points, consist of measures whose supports have at most n+2 points. Moreover, we use the Strassen and Kantorovich-Rubinstein duality theorems to develop representation...