……直观地说，测度为花体 F 中的每个事件 A 分配一个非负实数 P(A)。带符号测度允许负值。当然，有时候我们需要得到复数的测度。测度论可以参考，比如说，P. Halmos 的《Measure Theory》。Halmos 书的末尾对概率论、随机过程中的柯尔莫哥洛夫三级数定理等给出了非常精彩的介绍。想了解更多随机过程……
…Intuitively, a measure assigns to each event A in script F a non-negative real number P(A). A signed measure permits negative values. And of course at times want a measure that yields complex numbers. Measure theory is in, say, P. Halmos, Measure Theory. The back of Halmos has a really nice introduction to probability theory, the Kolmogorov three series theorem in stochastic processes, etc. For more in stochastic…
Halmos Measure Theory is a good prerequisite to Neveu. Rudin, Principles is a bit too little. Instead, the first half, the real half of Rudin's Real and Complex Analysis is a good prerequisite. So, is Royden's Real Analysis.…
…TeX, that σ^2 = \int (x - E[X])^2 dF_X(x) This integral need not be in the sense of Riemann (i.e., freshman calculus) because dF_X is a measure on the real line; so, the integral is in the sense of measure theory (see any of Rudin, Real and Complex Analysis; Royden, Real Analysis; Halmos, Measure Theory; Loève, Probability Theory). Sigma is defined for any random variable X or its distribution provided that E[X]…
……后来在随机过程方面，J. Doob（Halmos 的导师，后来成为冯·诺依曼的助手，等等）的著作以及 Halmos 的《Measure Theory》末尾关于概率的内容，让我对其肃然起敬。Halmos 在充分统计量和无偏估计方面的工作同样令人钦佩。我在 ML（机器学习）领域没见过这种水平的成果。你说外面有这种高质量的东西，但我看到的，比如 Ng 的……
…Then in stochastic processes I got some more respect from work of J. Doob (prof of Halmos who then became an assistant to von Neumann, etc.) and the material on probability in the back of the Halmos, Measure Theory. The Halmos work on sufficient statistics and unbiased estimation also deserved respect. I've seen no such quality from ML. You suggest that there is such quality out there, but what I saw, e.g., Ng's…
…control, I was interested in measurable selection and regular conditional distributions, and I got those from Breiman -- thanks Leo!!!! Yes, IIRC, there is the relevant Sierpinski exercise in Halmos, Measure Theory and also in Loeve, Probability, but it was Breiman who gave me what I really needed. (5) Generally Breiman is easy to read. He writes like he is trying to help the reader learn.
……直观地说，测度为花体 F 中的每个事件 A 分配一个非负实数 P(A)。带符号测度允许负值。当然，有时候我们需要得到复数的测度。测度论可以参考，比如说，P. Halmos 的《Measure Theory》。Halmos 书的末尾对概率论、随机过程中的柯尔莫哥洛夫三级数定理等给出了非常精彩的介绍。想了解更多随机过程……
…Intuitively, a measure assigns to each event A in script F a non-negative real number P(A). A signed measure permits negative values. And of course at times want a measure that yields complex numbers. Measure theory is in, say, P. Halmos, Measure Theory. The back of Halmos has a really nice introduction to probability theory, the Kolmogorov three series theorem in stochastic processes, etc. For more in stochastic…
Halmos 的《Measure Theory》是学习 Neveu 的绝佳前置读物。Rudin 的《Principles》（数学分析原理）内容稍微偏薄弱了点。相比之下，Rudin 的《Real and Complex Analysis》的前半部分（即实分析部分）是个很好的前置。Royden 的《Real Analysis》也很合适。……
Halmos Measure Theory is a good prerequisite to Neveu. Rudin, Principles is a bit too little. Instead, the first half, the real half of Rudin's Real and Complex Analysis is a good prerequisite. So, is Royden's Real Analysis.…
Rosenlicht。接着是《Linear Algebra Done Right》。然后是《Finite-Dimensional Vector Spaces》。Halmos 的《Measure Theory》。棒极了。
Rosenlicht. Linear Algbera done Right. Then Finite Dimensional Vector Spaces. Halmos' Measure Theory. Awesome.
……用 TeX 来说就是 σ^2 = \int (x - E[X])^2 dF_X(x)。这个积分不一定是黎曼意义上的（即大一微积分那种），因为 dF_X 是实数线上的测度；所以，该积分是测度论意义上的（参见 Rudin 的《Real and Complex Analysis》、Royden 的《Real Analysis》、Halmos 的《Measure Theory》、Loève 的《Probability Theory》中的任意一本）。Sigma 对任意随机变量 X 或其分布均有定义，前提是 E[X]……
…TeX, that σ^2 = \int (x - E[X])^2 dF_X(x) This integral need not be in the sense of Riemann (i.e., freshman calculus) because dF_X is a measure on the real line; so, the integral is in the sense of measure theory (see any of Rudin, Real and Complex Analysis; Royden, Real Analysis; Halmos, Measure Theory; Loève, Probability Theory). Sigma is defined for any random variable X or its distribution provided that E[X]…
……后来在随机过程方面，J. Doob（Halmos 的导师，后来成为冯·诺依曼的助手，等等）的著作以及 Halmos 的《Measure Theory》末尾关于概率的内容，让我对其肃然起敬。Halmos 在充分统计量和无偏估计方面的工作同样令人钦佩。我在 ML（机器学习）领域没见过这种水平的成果。你说外面有这种高质量的东西，但我看到的，比如 Ng 的……
…Then in stochastic processes I got some more respect from work of J. Doob (prof of Halmos who then became an assistant to von Neumann, etc.) and the material on probability in the back of the Halmos, Measure Theory. The Halmos work on sufficient statistics and unbiased estimation also deserved respect. I've seen no such quality from ML. You suggest that there is such quality out there, but what I saw, e.g., Ng's…
……控制，我对可测选择（measurable selection）和正则条件分布（regular conditional distributions）很感兴趣，我是从 Breiman 那里学到的——感谢 Leo！！！！是的，如果我没记错的话，Halmos 的《Measure Theory》以及 Loeve 的《Probability》里都有相关的谢尔宾斯基（Sierpinski）习题，但真正给我所需内容的是 Breiman。(5) 总的来说 Breiman 的书很好读。他的写作风格就好像是在全心全意帮读者学会一样。
…control, I was interested in measurable selection and regular conditional distributions, and I got those from Breiman -- thanks Leo!!!! Yes, IIRC, there is the relevant Sierpinski exercise in Halmos, Measure Theory and also in Loeve, Probability, but it was Breiman who gave me what I really needed. (5) Generally Breiman is easy to read. He writes like he is trying to help the reader learn.