It is our purpose in this paper to extend the notion of uniform convexity and uniform smoothness of Banach spaces to countably normed spaces.
Moreover in the Monge Ampère case, (k=n), we recover our definitions of uniform (A, G -convexity in [16], (called "uniform A-convexity with respect to G -convexityhinh extend the notion of uniform c-convexity with respect to a target domain (Omega ^*) in the optimal transportation case, as introduced in [16].
IN the late 1980's dedicated fashion followers took the notion of uniform dressing to heart, turning themselves out, almost identically, in a high-end variation on an officer's jacket from Chanel.
Had Kepler's investigation ended with the establishment of this architectonic principle, he might have continued to search for other sorts of harmonies; but his work would not have broken with the ancient Greek notion of uniform circular planetary motion.
The notion of uniform integrability plays the central role in establishing weak laws of large numbers.
Such dichotomies include for example the classical notion of uniform exponential dichotomies, as well as the notions of nonuniform exponential dichotomies and nonuniform polynomial dichotomies.
That is, we use the notion of uniform hyperbolicity for a family of periodic sequences of linear isomorphisms of R dim M. For this, we need several lemmas.
The notion of uniform pattern was proposed to take account of and give importance to those patterns which are most common and significant in texture classification.
It is well known that the notion of uniform integrability plays the central role in establishing weak laws of large numbers.
We further remark that the notion of uniform asymptotic regularity introduced by Edelstein and O'Brien [21] plays an important role for studying property ( A ) of nonlinear Lipschitzian-type operators.
