The Mathematics of ChanceCHANCE / MATHEMATICS

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Citations in the text have been restored at their original locations. Below, “original citation” means that the link was recovered from chat metadata; it does not mean that the entire content of every source was reverified in this restoration. The first four original identifiers have no recoverable URLs and are explicitly listed with supplementary sources checked during restoration; no original links have been fabricated. Images have been downloaded and embedded, so offline reading does not require loading the source websites.

  1. The link for the original identifier turn673477search0 could not be recovered. Supplementary sources checked during restoration: ETH Library: From games of chance to probability theory, MacTutor: Pascal. These two pages support the passage’s background on the early problem of points, the 1654 correspondence, and Huygens’s 1657 work; they do not establish which page each original identifier referred to.

  1. The link for the original identifier turn673477search2 could not be recovered. Supplementary sources checked during restoration: ETH Library: From games of chance to probability theory, MacTutor: Pascal. These two pages support the passage’s background on the early problem of points, the 1654 correspondence, and Huygens’s 1657 work; they do not establish which page each original identifier referred to.

  1. The link for the original identifier turn673477search4 could not be recovered. Supplementary sources checked during restoration: ETH Library: From games of chance to probability theory, MacTutor: Pascal. These two pages support the passage’s background on the early problem of points, the 1654 correspondence, and Huygens’s 1657 work; they do not establish which page each original identifier referred to.

  1. The link for the original identifier turn673477search7 could not be recovered. Supplementary sources checked during restoration: ETH Library: From games of chance to probability theory, MacTutor: Pascal. These two pages support the passage’s background on the early problem of points, the 1654 correspondence, and Huygens’s 1657 work; they do not establish which page each original identifier referred to.

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  1. Theorem 2.6 (Kolmogorov Extension Theorem). Given a set of compatible finite dimensional distributions \{\mu_{t_1\ldots t_m}\} with indexing set T, there exists a probability space (\Omega,\mathcal{F},\mathbb{P}) and a stochastic process \{X_t\} so that X_t has the required finite dimensional distributions, i.e. for all t_1 < \cdots < t_m \in T and A_1,\ldots,A_m \in \mathcal{B} we have. Original citation identifier: turn288123search38.

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Image Sources

Chapter 7: Convergence and Countable Probability

Chapter 8: Constructing Infinite Random Experiments

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