Egoroff's theorem - Open Access .click

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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

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

A stronger noncommutative Egoroff's theorem

, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Akemann, Charles A., Bagheri-Bardi, G.A.
openaire +2 more sources

On Egoroff's theorem [PDF]