偶然的数学CHANCE / MATHEMATICS

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引用与配图来源

正文引用按原位置恢复。以下“原引用”说明从聊天元数据恢复了链接,并不表示本次重新核验了每篇文献的全部内容。前四个原始标识没有可恢复的 URL,明确列为补核来源;没有伪造原链接。配图已下载嵌入,离线阅读不需要加载来源网站。

  1. 原始标识 turn673477search0 的链接未能恢复。本次补核:ETH 图书馆:From games of chance to probability theory、MacTutor:Pascal。这两页支持该段的早期赌金问题、1654年通信及1657年 Huygens 著作背景;不能据此判定原标识分别对应哪一页。

  1. 原始标识 turn673477search2 的链接未能恢复。本次补核:ETH 图书馆:From games of chance to probability theory、MacTutor:Pascal。这两页支持该段的早期赌金问题、1654年通信及1657年 Huygens 著作背景;不能据此判定原标识分别对应哪一页。

  1. 原始标识 turn673477search4 的链接未能恢复。本次补核:ETH 图书馆:From games of chance to probability theory、MacTutor:Pascal。这两页支持该段的早期赌金问题、1654年通信及1657年 Huygens 著作背景;不能据此判定原标识分别对应哪一页。

  1. 原始标识 turn673477search7 的链接未能恢复。本次补核:ETH 图书馆:From games of chance to probability theory、MacTutor:Pascal。这两页支持该段的早期赌金问题、1654年通信及1657年 Huygens 著作背景;不能据此判定原标识分别对应哪一页。

  1. A History of Probability and。原引用标识:turn689420search25。

  1. turn689420search2。原引用标识:turn689420search2。

  1. Studies in the History of Probability and Statistics I. Dicing and Gaming (A Note on。原引用标识:turn689420search26。

  1. Interpretations of Probability (Stanford Encyclopedia of Philosophy)。原引用标识:turn561005search0。

  1. Formal Epistemology (Stanford Encyclopedia of Philosophy)。原引用标识:turn561005search3。

  1. Classical definition of probability。原引用标识:turn561005search25。

  1. Tercentenary of Ars Conjectandi (1713): Jacob Bernoulli and the Founding of Mathematical Probability - Sylla - 2014 - International Statistical Review - Wiley Online Library。原引用标识:turn557906search0。

  1. The art of conjecturing (1692[?] published 1713) (Chapter 16) - The Emergence of Probability。原引用标识:turn557906search5。

  1. The first limit theorem (Chapter 17) - The Emergence of Probability。原引用标识:turn557906search11。

  1. Bernoulli theorem - Encyclopedia of Mathematics。原引用标识:turn557906search1。

  1. 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。原引用标识:turn557906search3。

  1. turn310466search0。原引用标识:turn310466search0。

  1. Thomas Bayes (1702 - 1761) - Biography - MacTutor History of Mathematics。原引用标识:turn310466search6。

  1. BULLETIN (New Series) OF THE。原引用标识:turn310466search24。

  1. Bayes Biography。原引用标识:turn310466search26。

  1. Was Bayes a Bayesian? - ScienceDirect。原引用标识:turn310466search8。

  1. Pierre-Simon Laplace (1749 - 1827) - Biography - MacTutor History of Mathematics。原引用标识:turn557906search12。

  1. Moivre。原引用标识:turn234816search0。

  1. De Moivre's Normal Approximation to the Binomial Distribution, 1733 - 1990 - Wiley Series in Probability and Statistics - Wiley Online Library。原引用标识:turn234816search4。

  1. JSS 18 (1) (1966) 2-15。原引用标识:turn234816search30。

  1. Abraham de Moivre (1667 - 1754) - Biography - MacTutor History of Mathematics。原引用标识:turn234816search3。

  1. A history of mathematical statistics from 1750 to 1930-Hald。原引用标识:turn234816search8。

  1. Classic Topics on The History of Modern Mathematical Statistics: From Laplace to More Recent Times | Mathematical Association of America。原引用标识:turn234816search6。

  1. A history of mathematical statistics from 1750 to 1930-Hald。原引用标识:turn523153search2。

  1. A short history of probability and statistics: 19th century。原引用标识:turn523153search1。

  1. Ellis on Mathematical Statistics and Probability | Springer Nature Link。原引用标识:turn234816search7。

  1. August 1827: Robert Brown and Molecular Motion in a Pollen-filled Puddle | American Physical Society。原引用标识:turn360592search6。

  1. Controlling the Unobservable: Experimental Strategies and Hypotheses in Discovering the Causal Origin of Brownian Movement | Springer Nature Link。原引用标识:turn360592search7。

  1. The case of Brownian motion | The British Journal for the History of Science | Cambridge Core。原引用标识:turn360592search3。

  1. HISTORICAL BACKGROUND | Brownian Motion: Fluctuations, Dynamics, and Applications | Oxford Academic。原引用标识:turn360592search4。

  1. 111 years of Brownian motion - PMC。原引用标识:turn360592search5。

  1. Bachelier, Louis (1870–1946) - Bru - Major Reference Works - Wiley Online Library。原引用标识:turn360592search8。

  1. Brownian motion (Chapter 3) - Brownian Motion, Hardy Spaces and Bounded Mean Oscillation。原引用标识:turn360592search0。

  1. Donsker invariance principle - Encyclopedia of Mathematics。原引用标识:turn288123search2。

  1. Lecture 14: Brownian Motion。原引用标识:turn288123search41。

  1. Advanced Probability。原引用标识:turn288123search39。

  1. 2.5 Kolmogorov Continuity Theorem.。原引用标识:turn288123search36。

  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。原引用标识:turn288123search38。

  1. Partial Differential Equations and Diffusion Processes。原引用标识:turn516523search36。

  1. AMS :: Notices of the American Mathematical Society。原引用标识:turn516523search1。

  1. Stochastic Processes。原引用标识:turn516523search41。

  1. 1. LECTURE 1: APRIL 3, 2012。原引用标识:turn288123search37。

  1. The Early Development of Set Theory (Stanford Encyclopedia of Philosophy)。原引用标识:turn701804search1。

  1. Studies in the history of probability and statistics XLVI. Measure into probability: from Lebesgue to Kolmogorov | Biometrika | Oxford Academic。原引用标识:turn701804search0。

  1. On the problem of measuring sets of points by Giuseppe Vitali。原引用标识:turn701804search4。

  1. Elementary Real Analysis。原引用标识:turn701804search35。

  1. From the beginning of set theory to Lebesgue’s measure problem。原引用标识:turn701804search39。

  1. Lebesgue Measure · Guidebook 3A.2 · Neckpinch。原引用标识:turn701804search6。

  1. Foundations of Quantitative。原引用标识:turn701804search37。

  1. 7. The 20th C and Measure Theory。原引用标识:turn701804search40。

  1. Henri Lebesgue (1875 - 1941) - Biography - MacTutor History of Mathematics。原引用标识:turn817174search1。

  1. Henri Lebesgue and the Development of the Integral Concept*。原引用标识:turn817174search26。

  1. Jal Choksi - A history of the convergence theorems of (Lebesgue) integration。原引用标识:turn817174search0。

  1. Modes of Convergence。原引用标识:turn477144search24。

  1. Probability: Limit Theorems I。原引用标识:turn477144search25。

配图来源

第七章:收敛与可数概率

第八章:无限随机实验的构造