the metrization of statistical metric spaces - Project Euclid
Recommend Documents
F. S. de Blasi â L. Górniewicz â G. Pianigiani. Dedicated to Andrzej ... subsets of Z. For z â Z and r > 0, BZ(z, r) stands for an open ball in Z with center z and ...
the Cartan formula for secondary operations, [7], and a particular factorization of the cube of a certain 8-dimensional cohomology class,. [10], to show that Hl5{X) ...
In other words, we have to consider N = 2 superconformal theory living on the world-sheet and ... the complex orthogonal group and (C* denotes the group of non-zero complex numbers. ... define a field of type Ton the superconformal manifold as a fc-c
Proof. In III.5 let n = dim/(if) - 1. Proof of III.2. We simply apply III.6 inductively in the following manner. Letm1 = min {μ(y): yef(K)}. Then if k = 0 we are finished.
A property is said to hold p-quasi everywhere, or p-q.e., if that property holds for all points outside a set of zero p-capacity. A function is said to be p-quasi ...
Furthermore, the sequence vj converges to u in N1,p(X). Proof. Let x, y be two points .... loc âCapp(E,F) if E and F are disjoint compact subsets of X. Here Modp(E ...
3 Department of Mathematics, Hashemite University, Zarqa, Jordan. Correspondence should be addressed to Erdal Karapınar, [email protected].
Partial answers were known since Pfister [6] proved that every precompact set in a (DF)-space is metrizable by using the fact that a lcs E is trans-separable if and.
associated with an irreducible representation $\delta$ .... $C^{\infty}(\Sigma)=\sum_{m,n\geq 0}\ovalbox{\tt\small REJECT}^{m}(R^{dp})\otimes\ovalbox{\tt\small ..... $=\frac{1}{\pi}\int_{-\pi/2}^{\pi/2}(\cos\theta)^{\lambda}e^{-il\theta}d\theta$.
PAUL F. DUVALL, PETER FLETCHER AND ROBERT A. MCCOY. This paper ..... P. Fletcher and R. L. Snider, Topological Galois spaces, Fund. Math., 68 (1970) ...
R. MICHAEL RANGE. The boundary behavior of proper ... which are defined on Dε, satisfy, for each keN, an estimate | labile* ^ ^ r * I WL~ ^z-ε), where 0
Apr 24, 2006 - JIMMIE LAWSON and YONGDO LIM. (Received ... Introduction. Let A be a unital C£-algebra with identity e, and let A+ be the set of positive.
... A convenient category of topological spaces, Michigan. Math. J. 14 (1967), 133-152. MR 35: 970. HOFSTRA UNIVERSITY, HEMPSTEAD, NEW YORK 11550.
We derive fast rates of convergence for the excess risk of empirical risk ..... case, we use kernel deconvolution estimators in the empirical risk minimization.
Feb 23, 1984 - hyperbolicity introduced by Ehrenpreis [4, Theorem 2] for Schwartz dis- ..... Paley-Weiner theorem to e D and using (17), it follows that the ...
A topological property & is called a Hausdorff extension property if each Hausdorff space X can be densely embedded in a space κ&Xsuch that (1) κ&X is a ...
These are all elements of A. It is easy to see that. (3.1.iii) p ..... pap by uniqueness or polar decompositions. A direct calculation shows that a has the form with u.
Oct 3, 2005 - MAR IA J. RIVERA ... see, this extension carries new problems, the solution of which is here ... From the Bartle-Dunford-Schwartz theorem, ... With respect to the Banach lattices theory we refer to [8, 11]. We ... 2. Spaces of (Φ )-qua
with an Appendix by Mark Dickinson & Krishnan Shankar. Introduction ...... manifolds, smoothings, and triangulations (with notes by John Milnor and. Michael ...
Dec 4, 1991 - the blow up of A, the unfolding (in fact, the resolution of singularities of ..... fact that the family {C face of A/C c (dim C)-skeleton of V} is totally.
Conjugate Banach spaces isomorphic to complemented subspaces of LI(~), ..... norm ]{/11 = ~r~r I/(7) 1" By the unit-vectors-basis of li(r) (resp. c0(F)) we refer to ...... subspace of LI(~), we may choose an i such that 11i = m, by a recent result of
Since dimP(F,)=card F,
is an extension to metric spaces of the absolute continuity property on almost all lines of .... (v) If u â N1,p(X) and v is a bounded Lipschitz continuous function,.
Abstract. This paper introduces a new construction for q-ary equidistant code C with rank metric where q is a power of 2. Investigations on structural properties of ...
the metrization of statistical metric spaces - Project Euclid
that a statistical metric induces a natural topology for the space on which it is .... (if unique) of the statistical distances each form metric spaces; and similarly, in a ...
THE METRIZATION OF STATISTICAL METRIC SPACES B. SCHWEIZER, A. SKLAR AND E. THORP
In a previous paper on statistical metric spaces [3] it was shown that a statistical metric induces a natural topology for the space on which it is defined and that with this topology a large class of statistical metric (briefly, SM) spaces are Hausdorff spaces. In this paper we show that this result (Theorem 7.2 of [3]) can be considerably generalized. In addition, as an immediate corollary of this generalization, we prove that with the given topology a large number of SM spaces are metrizable, i.e., that in numerous instances the existence 1 of a statistical metric implies the existence of an ordinary metric. THEOREM I . 2 parameter
Let (S, J^~) be a statistical
collection
of subsets
ofSxS
metric
defined
space, 0 , λ > 0} ,
where U(e, λ) - {(p, q); p, q in S and Fpq(e) > 1 - λ} , and T a two-place function from [0, 1] x [0, 1] to [0, 1] satisfying T(c, d)^ T(α, b) for c ϋ> α, d ^ b and sup x
