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Almost everywhere convergence of convolution measures [PDF]

, 2009
Let $(X,\mathcal{B},m,\tau)$ be a dynamical system with $(X,\mathcal{B},m)$ a probability space and $\tau$ a measurable, invertible, measure preserving transformation.
Savvopoulou, Anna K
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Almost Everywhere Convergence

2016
We have seen in Part II the importance of a.e. convergence in integration theory. The purpose of this last chapter of our book is to clarify its relationship to other convergence notions.
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Almost everywhere convergence in MV-algebras with product

Soft Computing, 2001
This is a short technical paper in which the author generalizes some limit constructions in probability (almost everywhere convergence of random functions). The classical probability space is generalized to a probability MV-algebra \((M,m)\), where \(M\) is a \(\sigma\)-complete MV-algebra with product and \(m\) is a faithful state, and a classical ...
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THE PRINCIPLE OF CONVERGENCE "ALMOST EVERYWHERE" IN LIE GROUPS

Mathematics of the USSR-Sbornik, 1973
Let U be a neighborhood of the identity in an arbitrary Lie group with a fixed system of local coordinates (x) and let be independent random variables taking values in the neighborhood U and be real variables naturally induced by the variables in the system of local coordinates (x).
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Almost everywhere convergence of Fourier integrals

Archiv der Mathematik, 1995
In this paper, we prove that if \(f \in L^ p (\mathbb{R}^ n)\), for certain \(p\) and \(n\), satisfies \[ \lim_{\lambda \downarrow 1} \varlimsup_{R \to \infty} \int_{R < | \xi | \leq \lambda R} \bigl | \widehat f(\xi) \bigr | d \xi = 0, \] then, for almost all \(x \in \mathbb{R}^ n\), \(\int_{| \xi | \leq R} \widehat f (\xi) e^{ix \cdot \xi} d \xi ...
Chen, Chang-Pao, Lin, Chin-Cheng
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Remarks on Almost Everywhere Convergence and Approximate Identities

Acta Mathematica Sinica, English Series
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Douglas, Sean, Grafakos, Loukas
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Uniqueness of Almost Everywhere Convergent Vilenkin Series

Canadian Mathematical Bulletin, 2004
AbstractD. J. Grubb [3] has shown that uniqueness holds, under a mild growth condition, for Vilenkin series which converge almost everywhere to zero. We show that, under even less restrictive growth conditions, one can replace the limit function 0 by an arbitrary f ∈ Lq, when q > 1.
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Almost everywhere convergence of convolution powers

Ergodic Theory and Dynamical Systems, 1994
AbstractGiven an ergodic dynamical system (X,B,m, τ) and a probability measure μ on the integers, define for all f ∈ L1(X) The almost everywhere convergence of the convolution powers μnf(x) depends on the properties of μ. If μ has finite and then for all f ∈ Lp(X), 1< p < ∞, exists for a.e. x.
Bellow, Alexandra, Jones, Roger, Rosenblatt, Joseph   +2 more
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Stability of unconditional convergence almost everywhere

Mathematical Notes of the Academy of Sciences of the USSR, 1973
We will investigate the properties of series of functions which are unconditionally convergent almost everywhere on [0, 1]. We will establish the following theorem: If the series σ k=1 ∞ f k(x) converges unconditionally almost everywhere, then there exists a sequence {Βk} 1
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Almost everywhere convergence of weighted averages

Mathematische Annalen, 1992
Given a sequence \((\mu_ n)\) of probability measures on \(Z\), and an invertible measure-preserving transformation \(\tau\) of a probability space \((X,\beta,m)\), the averages \(\mu_ nf(x)=\sum^{\infty}_{k=- \infty}\mu_ n(k)f(\tau^ kx)\) are bounded operators on \(L^ p(m)\), \(1\leq p\leq\infty\).
Bellow, Alexandra, Jones, Roger L., Rosenblatt, Joseph   +2 more
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