Results 21 to 30 of about 107 (76)

Best Approximation of Data Distributed in a Band

International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011
We study the problem to approximate a data set which are affected in a such way that they present us as a band in the plane. We introduce a deviation measure, and we research the asymptotic behavior of the best approximants when the band shrink in some sense.
H. Cuenya, F. Levis, C. Rodriguez, J. Jahn   +3 more
wiley   +1 more source

Sign‐changing and multiple solutions for the p‐Laplacian

Abstract and Applied Analysis, Volume 7, Issue 12, Page 613-625, 2002., 2002
We obtain a positive solution, a negative solution, and a sign‐changing solution for a class of p‐Laplacian problems with jumping nonlinearities using variational and super‐subsolution methods.
Siegfried Carl, Kanishka Perera
wiley   +1 more source

On Iterated Limits of Measurable Mappings

, 1965
Egoroff' s theorem [1] was extended by Kvačko [3] to functions with values in a separable metric space; and, as is easily seen, this result applies also to separable pseudometric spaces.
Elias Zakon
core   +1 more source

Limiting behavior of the perturbed empirical distribution functions evaluated at U‐statistics for strongly mixing sequences of random variables

International Journal of Stochastic Analysis, Volume 10, Issue 1, Page 3-20, 1997., 1996
We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic for a class of strongly mixing sequences of random variables {Xi, i ≥ 1}. Stationarity is not assumed. Here is the perturbed empirical distribution function and Un is a U‐statistic based on X1, …, Xn.
Shan Sun, Ching-Yuan Chiang
wiley   +1 more source

On the Radon-Nikodým theorem and locally convex spaces with the Radon-Nikodým property

, 1977
Let F be a quasi-complete locally convex space, ( Ω , Σ , μ ) (\Omega ,\Sigma ,\mu ) a complete probability space, and L 1
G. Y. H. Chi
core   +1 more source

Fundamental theorem of Wiener calculus

International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 3, Page 443-452, 1990., 1990
In this paper we define and develop a theory of differentiation in Wiener space C[0, T]. We then proceed to establish a fundamental theorem of the integral calculus for C[0, T]. First of all, we show that the derivative of the indefinite Wiener integral exists and equals the integrand functional.
Chull Park, David Skoug, Lawrence Smolowitz   +2 more
wiley   +1 more source

Carnot rectifiability and Alberti representations

Proceedings of the London Mathematical Society, Volume 130, Issue 1, January 2025.
Abstract A metric measure space is said to be Carnot‐rectifiable if it can be covered up to a null set by countably many bi‐Lipschitz images of compact sets of a fixed Carnot group. In this paper, we give several characterisations of such notion of rectifiability both in terms of Alberti representations of the measure and in terms of differentiability ...
G. Antonelli, E. Le Donne, A. Merlo
wiley   +1 more source

Fuzzy sets and small systems [PDF]

, 2013
summary:Independently with [7] a corresponding fuzzy approach has been developed in [3-5] with applications in measure theory. One of the results the Egoroff theorem has been proved in an abstract form.
Považan, Jaroslav, Riečan, Beloslav
core  

Lebesgue-type convergence theorems in Banach lattices with applications to compact operators

, 1979
The main result is a Lebesgue-type convergence theorem in the setting of Banach lattices, of which the classical Lebesgue dominated convergence theorem is the prime example.
van Eldik, P., Grobler, J.J.
core   +1 more source

On Almost Uniform Convergence of Families of Functions

, 1964
In [5] Tolstov showed by a counterexample that Egoroff' s theorem on almost uniform convergence cannot be extended to families of functions (ft(x)}, with t a continuous real parameter.
Elias Zakon
core   +1 more source