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3 results

  • Appendix - A Rapid Review of Sets and Probability

  • David C. Vella, Skidmore College, New York
  • Book:
    Invitation to Linear Programming and Game Theory
    Published online:
    11 March 2021
    Print publication:
    11 March 2021, pp 480-517

  • Summary

    In this appendix, we collect together some basic material that readers should know before studying this book. The material includes sets, enumeration, and probability. In practice, we have found that students have often already been exposed to this material and only need a quick review, so we did not want to include another introductory chapter delaying the study of our main topics. We cover sets, subsets, universal sets, unions,intersections and complements, Cartesian products, power sets, and rules such as De Morgan's laws. For enumeration, we cover the addition and multiplications rules and special cases such as permutations and combinations. For probability, although our coverage is less detailed than other chapters, we actually cover more than we need for the rest of the book, including conditional probability and Bayes's theorem. Most readers will be comfortable just using this chapter as a reference or review.

  • RESOLVABILITY OF MEASURABLE SPACES

  • Part of
  • GRAŻYNA HORBACZEWSKA, SEBASTIAN LINDNER
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 94 / Issue 1 / August 2016
    Published online by Cambridge University Press:
    11 January 2016, pp. 70-79
    Print publication:
    August 2016
    • Article
      • You have access
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  • We consider a special kind of structure resolvability and irresolvability for measurable spaces and discuss analogues of the criteria for topological resolvability and irresolvability.

  • On sets not belonging to algebras

  • L. Š. Grinblat
  • Journal:
    The Journal of Symbolic Logic / Volume 72 / Issue 2 / June 2007
    Published online by Cambridge University Press:
    12 March 2014, pp. 483-500
    Print publication:
    June 2007

  • Let be a finite sequence of algebras of sets given on a set with more than pairwise disjoint sets not belonging to It was shown in [4] and [5] that in this case Let us consider, instead a finite sequence of algebras It turns out that if for each natural i ≤ l there exist no less than pairwise disjoint sets not belonging to then But if l ≥ 195 and if for each natural i ≤ l there exist no less than pairwise disjoint sets not belonging to then After consideration of finite sequences of algebras, it is natural to consider countable sequences of algebras. We obtained two essentially important theorems on a countable sequence of almost σ-algebras (the concept of almost σ-algebra was introduced in [4]).