References and Image Sources

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.

2. 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.

3. 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.

4. 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.

5. A History of Probability and. Original citation identifier: turn689420search25.

6. turn689420search2. Original citation identifier: turn689420search2.

7. Studies in the History of Probability and Statistics I. Dicing and Gaming (A Note on. Original citation identifier: turn689420search26.

8. Interpretations of Probability (Stanford Encyclopedia of Philosophy). Original citation identifier: turn561005search0.

9. Formal Epistemology (Stanford Encyclopedia of Philosophy). Original citation identifier: turn561005search3.

10. Classical definition of probability. Original citation identifier: turn561005search25.

11. Tercentenary of Ars Conjectandi (1713): Jacob Bernoulli and the Founding of Mathematical Probability - Sylla - 2014 - International Statistical Review - Wiley Online Library. Original citation identifier: turn557906search0.

12. The art of conjecturing (1692[?] published 1713) (Chapter 16) - The Emergence of Probability. Original citation identifier: turn557906search5.

13. The first limit theorem (Chapter 17) - The Emergence of Probability. Original citation identifier: turn557906search11.

14. Bernoulli theorem - Encyclopedia of Mathematics. Original citation identifier: turn557906search1.

15. An Essay towards Solving a Problem in the Doctrine of Chances. By the Late Rev. Mr. Bayes, F. R. S. Communicated by Mr. Price, in a Letter to John Canton, A. M. F. R. S. | JSTOR. Original citation identifier: turn557906search3.

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17. Thomas Bayes (1702 - 1761) - Biography - MacTutor History of Mathematics. Original citation identifier: turn310466search6.

18. BULLETIN (New Series) OF THE. Original citation identifier: turn310466search24.

19. Bayes Biography. Original citation identifier: turn310466search26.

20. Was Bayes a Bayesian? - ScienceDirect. Original citation identifier: turn310466search8.

21. Pierre-Simon Laplace (1749 - 1827) - Biography - MacTutor History of Mathematics. Original citation identifier: turn557906search12.

22. Moivre. Original citation identifier: turn234816search0.

23. De Moivre's Normal Approximation to the Binomial Distribution, 1733 - 1990 - Wiley Series in Probability and Statistics - Wiley Online Library. Original citation identifier: turn234816search4.

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25. Abraham de Moivre (1667 - 1754) - Biography - MacTutor History of Mathematics. Original citation identifier: turn234816search3.

26. A history of mathematical statistics from 1750 to 1930-Hald. Original citation identifier: turn234816search8.

27. Classic Topics on The History of Modern Mathematical Statistics: From Laplace to More Recent Times | Mathematical Association of America. Original citation identifier: turn234816search6.

28. A history of mathematical statistics from 1750 to 1930-Hald. Original citation identifier: turn523153search2.

29. A short history of probability and statistics: 19th century. Original citation identifier: turn523153search1.

30. Ellis on Mathematical Statistics and Probability | Springer Nature Link. Original citation identifier: turn234816search7.

31. August 1827: Robert Brown and Molecular Motion in a Pollen-filled Puddle | American Physical Society. Original citation identifier: turn360592search6.

32. Controlling the Unobservable: Experimental Strategies and Hypotheses in Discovering the Causal Origin of Brownian Movement | Springer Nature Link. Original citation identifier: turn360592search7.

33. The case of Brownian motion | The British Journal for the History of Science | Cambridge Core. Original citation identifier: turn360592search3.

34. HISTORICAL BACKGROUND | Brownian Motion: Fluctuations, Dynamics, and Applications | Oxford Academic. Original citation identifier: turn360592search4.

35. 111 years of Brownian motion - PMC. Original citation identifier: turn360592search5.

36. Bachelier, Louis (1870–1946) - Bru - Major Reference Works - Wiley Online Library. Original citation identifier: turn360592search8.

37. Brownian motion (Chapter 3) - Brownian Motion, Hardy Spaces and Bounded Mean Oscillation. Original citation identifier: turn360592search0.

38. Donsker invariance principle - Encyclopedia of Mathematics. Original citation identifier: turn288123search2.

39. Lecture 14: Brownian Motion. Original citation identifier: turn288123search41.

40. Advanced Probability. Original citation identifier: turn288123search39.

41. 2.5 Kolmogorov Continuity Theorem.. Original citation identifier: turn288123search36.

42. 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.

43. Partial Differential Equations and Diffusion Processes. Original citation identifier: turn516523search36.

44. AMS :: Notices of the American Mathematical Society. Original citation identifier: turn516523search1.

45. Stochastic Processes. Original citation identifier: turn516523search41.

46. 1. LECTURE 1: APRIL 3, 2012. Original citation identifier: turn288123search37.

47. The Early Development of Set Theory (Stanford Encyclopedia of Philosophy). Original citation identifier: turn701804search1.

48. Studies in the history of probability and statistics XLVI. Measure into probability: from Lebesgue to Kolmogorov | Biometrika | Oxford Academic. Original citation identifier: turn701804search0.

49. On the problem of measuring sets of points by Giuseppe Vitali. Original citation identifier: turn701804search4.

50. Elementary Real Analysis. Original citation identifier: turn701804search35.

51. From the beginning of set theory to Lebesgue’s measure problem. Original citation identifier: turn701804search39.

52. Lebesgue Measure · Guidebook 3A.2 · Neckpinch. Original citation identifier: turn701804search6.

53. Foundations of Quantitative. Original citation identifier: turn701804search37.

54. 7. The 20th C and Measure Theory. Original citation identifier: turn701804search40.

55. Henri Lebesgue (1875 - 1941) - Biography - MacTutor History of Mathematics. Original citation identifier: turn817174search1.

56. Henri Lebesgue and the Development of the Integral Concept*. Original citation identifier: turn817174search26.

57. Jal Choksi - A history of the convergence theorems of (Lebesgue) integration. Original citation identifier: turn817174search0.

58. Modes of Convergence. Original citation identifier: turn477144search24.

59. Probability: Limit Theorems I. Original citation identifier: turn477144search25.

Image Sources

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Chapter 7: Convergence and Countable Probability

• Émile Borel (1909), Les probabilités dénombrables et leurs applications arithmétiques, Rendiconti 27, 247–271. Publication record.
• F. P. Cantelli (1917), Sulla probabilità come limite della frequenza. Original academy catalog.
• F. P. Cantelli (1935), Considérations sur la convergence dans le Calcul des probabilités, Annales IHP 5, 3–50. Original text.
• Olav Kallenberg (2021), Foundations of Modern Probability, third edition. Official book record.

Chapter 8: Constructing Infinite Random Experiments

• A. Kolmogoroff (1933), Grundbegriffe der Wahrscheinlichkeitsrechnung. Publisher’s record and table of contents for the original book. The original book’s year and table of contents were checked. The date of a modern online edition is not presented as its original publication date, and no claim is made to reproduce all of the original book’s proofs.
• P. J. Daniell (1919), Integrals in An Infinite Number of Dimensions, Annals of Mathematics 20(4), 281–288. Original journal record. Bibliographic information was checked; the chapter’s modern cylinder-set proof is not attributed to this paper as its original proof.