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Some Results in Pointwise Ergodic Theory

  • Author(s): Krause, Benjamin
  • Advisor(s): Tao, Terence
  • et al.

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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