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Almost Everywhere Convergence Of Weighted Ergodic Averages, Christopher Michael Wedrychowicz
Almost Everywhere Convergence Of Weighted Ergodic Averages, Christopher Michael Wedrychowicz
Legacy Theses & Dissertations (2009 - 2024)
Let $(X,\mathcal{B},\lambda,T)$ be a dynamical system and $\mbox{Log}_{(n)}x$
Almost Everywhere Convergence Of Convolution Measures, Anna K. Savvopoulou
Almost Everywhere Convergence Of Convolution Measures, Anna K. Savvopoulou
Legacy Theses & Dissertations (2009 - 2024)
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. The present thesis deals with the almost everywhere convergence in $\mbox{L}^1(X)$ of a sequence of operators of weighted averages. Almost everywhere convergence follows once we obtain an appropriate maximal estimate and once we provide a dense class where convergence holds almost everywhere. The weights are convolution products of members of a sequence of probability measures $\{\nu_i\}$ on $\mathbb{Z}$. In the last section, we also prove a variation inequality for this type of sequence operators.