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Background Results

Statements of results from the literature that are cited in later chapters of the dissertation, numbered as in the dissertation PDF.

References
  1. Mattila, P. (2015). Preliminaries and Some Simpler Applications of the Fourier Transform. In Fourier Analysis and Hausdorff Dimension (pp. 9–10). Cambridge University Press.
  2. Orponen, T. (2021). Combinatorial proofs of two theorems of Lutz and Stull. Mathematical Proceedings of the Cambridge Philosophical Society, 171(3), 503–514. 10.1017/s0305004120000328
  3. Stull, D. M. (2022). Pinned Distance Sets Using Effective Dimension. https://arxiv.org/abs/2207.12501
  4. Altaf, I., Bushling, R., & Wilson, B. (2023). Distance sets bounds for polyhedral norms via effective dimension.
  5. Kechris, A. S. (1995). Classical Descriptive Set Theory (1st ed., Vol. 156, p. XVIII, 404). Springer-Verlag New York, Inc. 10.1007/978-1-4612-4190-4
Chapter 2: Robustness of Conditional Kolmogorov Complexity
2.2 Effective Dimension under Uniformly Continuous Maps