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  • 14 - Contrasts between Category and Measure

  • N. H. Bingham, Imperial College London, Adam J. Ostaszewski, London School of Economics and Political Science
  • Book:
    Category and Measure
    Published online:
    14 January 2025
    Print publication:
    23 January 2025, pp 222-234

  • Summary

    As a counterpart to Chapter 9 on category–measure duality, we focus here on a variety of situations in which duality fails. We cover a range of topics: Liouville numbers, Banach–Tarski (‘paradoxical’) decompositions, restriction and continuity, random series, normal numbers, topological and Hausdorff dimension, random Dirichlet series, filters, genericity, the Fubini and Kuratowski–Ulam theorems. We give an account of modern results on forcing, deferring technicalities to Chapter 16.