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Some Results in Pointwise Ergodic Theory


In this dissertation we establish various pointwise ergodic theorems, of both quanitative and qualitative nature. Beyond an introductory chapter, we devote one chapter to establishing quantitative ergodic theorems for $\Z^d$ actions; one chapter to quantitative ergodic theorems for polynomial orbits; one chapter to uniform estimates for various modulated ergodic averages; and the final chapter to random modulated averages.

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