The semigroup-valued integral of M. Sion [S] is reformulated for a general notion of approximation by sums of values taken by a set function integrand. A convergence in measure theorem is established, which yields both his pointwise dominated convergence theorem as well as an integrability criterion which specializes to his existence theorem. In [S] M. Sion introduced and developed an "integral...

Uniform filter bank approach can be considered to perform independent component analysis (ICA) for convolved mixtures. It achieves better separation performance than the frequency domain approach and gives faster convergence speed with less computational complexity than the time domain approach. However, when the uniform filter bank approach is applied to natural audio signals, for high frequen...

.z I < p(e), E < p(E) < Po, and p(c) depends not only on e but also on w(z). The function p(E) clearly decreases monotonically with e; it also approaches zero with e, for the transformation z(w), although multiple-valued, is continuous. If now E(e) lies in Jz < E, E < Eo, then the convex hull of w(E(e)) contains the point w+, and the m antecedents z+ of w+ in jz < Po defined by equation (5) lie...

5.3 Approximating Stochastic Concepts by Functions ............................... 88 5.4 Classification Noise and Semi-Consistent Learning ..............................96 6. N on-U niform L earnab ility ...........................................................................98 6.1 The Notion of Non-Uniform L earnab ility ................................................98 6.2 Distribution-I...

We study the robustness of interim correlated rationalizability to perturbations of higher-order beliefs. We introduce a new metric topology on the universal type space, called uniform-weak topology, under which two types are close if they have similar first-order beliefs, attach similar probabilities to other players having similar first-order beliefs, and so on, where the degree of similarity...

This paper is devoted to the convergence rate estimate for the method of successive subspace corrections applied to symmetric and positive semidefinite (singular) problems. In a general Hilbert space setting, a convergence rate identity is obtained for the method of subspace corrections in terms of the subspace solvers. As an illustration, the new abstract theory is used to show uniform converg...

Consider a class of skew product transformations consisting of an ergodic or a periodic transformation on a probability space (M,B, μ) in the base and a semigroup of transformations on another probability space (Ω,F , P ) in the fibre. Under suitable mixing conditions for the fibre transformation, we show that the properties ergodicity, weakly mixing, and strongly mixing are passed on from the ...

This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result for the mentioned systems of equations are obtained as an application of a basic approximation result, which is formulated entirely in terms of usual real va...

In this paper we obtain almost sure convergence theorems for vectorvalued uniform amarts and C-sequences without assuming the Radon-Nikodym Property. Specifically, it is shown that if a limit exists in a weak sense for these martingale generalizations, then a.s. scalar and strong convergence follow. These results lead to some new versions of the Ito-Nisio theorem. Convergence results for random...