实分析与复分析

Hacker News 上怎么说

• ten_fingers · 2012 年

  …为概率论、随机过程和统计学打下了扎实清晰的基础。测度论最舒服的入门教材大概就是 Royden 的《Real Analysis》了。Rudin 的《Real and Complex Analysis》讲实分析的前半部分也很不错，对 Hilbert 空间和 Banach 空间都做了很好的介绍，对傅里叶变换的处理也很精彩。在基于测度论的概率论领域，我最喜欢的作者是 J. Neveu（这本很长…

  …makes a clean foundation for probability, stochastic processes, and statistics. Likely the nicest first text in measure theory is Royden's 'Real Analysis'. Also good is the first, real, half of Rudin's 'Real and Complex Analysis' where he also gives nice introductions to both Hilbert and Banach spaces and a nice treatment of the Fourier transform. My favorite authors in probability based on measure theory are J. Neveu (long…

• fermigier · 2022 年

  物理学：费曼物理学讲义。数学：Rudin 的《真实分析与复分析》。软件工程：《人月神话》。计算机科学：Knuth 的《计算机程序设计艺术》（TAOCP）。

  Physics: Feynman's lectures on physics. Maths: Rudin's Real and Complex analysis. Software engineering: The Mythical Man-Month. Computer science: Knuth's TAOCP.

• HilbertSpace · 2009 年

  …定理，以及 Hilbert 和 Banach 空间。长期以来广受好评、出自斯坦福、有时针对统计专业学生的教材是 Royden 的《Real Analysis》。写得太美了。另外也应该读读 Rudin《Real and Complex Analysis》里的实分析部分；它的难度比 baby Rudin 上升了几个台阶。再次提醒：找个好老师开的好课，能带你把内容顺下来而不至于卡壳。然后再回头去啃教材…

  …theorem, and Hilbert and Banach spaces. Long popular, from Stanford and sometimes aimed at statistics students, is Royden, 'Real Analysis'. It's gorgeous. Should also read the real half of Rudin, 'Real and Complex Analysis'; it's a few steps up in difficulty from baby Rudin. Again, hint: Get a good course from a good teacher who can get you over the material without getting stuck. Then go back and study the material…

• graycat · 2016 年

  …那么 f 在 [0,1] 上的黎曼积分不存在，但测度论积分存在且结果为 0。目前至少有两本经典教材：Royden 的《Real Analysis》和 Rudin 的《Real and Complex Analysis》。不过优秀的教材还有很多，而且之后可能还会有更多佳作。读 Rudin 的话，后半部分复变函数完全可以略过不看。Royden 读起来更容易。Rudin 的数学表述则更加凝练精简。…

  …Then the Riemann integral of f over [0,1] does not exist, but the measure theory integral does and gives 0 for the result. There are at least two now classic books, Royden, Real Analysis and Rudin, Real and Complex Analysis. But there are more, and likely more can be written. For Rudin, can f'get about the last half on functions of a complex variable. Royden is easier to read. Rudin has the math more succinctly presented.…

• eyphka · 2022 年

  …学生。:) 要想打牢微积分的基础，并让自己成为更厉害的数学人，一个很好的起点是 -> Baby Rudin（Walter Rudin 的《Principles of Mathematical Analysis》） Papa Rudin（Walter Rudin 的《Real and Complex Analysis》） Grandpa Rudin（Walter Rudin 的《Functional Analysis》）

  …students. :) For a foundational understanding of Calculus, and just becoming a better mathematician, a good start would be -> Baby Rudin (Principles of Mathematical Analysis, Walter Rudin) Papa Rudin (Real and Complex Analysis, Walter Rudin) Grandpa Rudin (Functional Analysis, Walter Rudin)

• graycat · 2015 年

  …对充分统计量的根本性贡献。没记错的话（IIRC），Halmos 是在芝加哥大学写出《Measure Theory》的。关于测度论的详尽细节和更多内容，可以参考比如 H. Royden 的《Real Analysis》和 W. Rudin 的《Real and Complex Analysis》。要将测度论聚焦到概率论，可以用我列出的那些作者的著名教材，比如 Loève……Royden 和 Rudin 是学 Loève 等人著作的绝佳先修课。通常，事件的 sigma 代数…

  …the fundamental contribution to sufficient statistics. IIRC, it was at Chicago that Halmos wrote Measure Theory. Great details on measure theory and much more are in, say, H. Royden, Real Analysis and W. Rudin, Real and Complex Analysis. To narrow measure theory to probability theory, use the famous texts by the authors I listed, Loeve, .... Royden and Rudin are terrific prerequisites to Loeve, etc. Commonly the sigma algebra of events…

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