Math 6710 lecture notes
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چکیده
Caution! These lecture notes are very rough. They are mainly intended for my own use during lecture. They almost surely contain errors and typos, and tend to be written in a stream-of-consciousness style. In many cases details, precise statements, and proofs are left to Durrett’s text, homework or presentations. But perhaps these notes will be useful as a reminder of what was done in lecture. If I do something that is substantially different from Durrett I will put it in here. Thursday, August 23 Overview: Probability: study of randomness. Questions whose answer is not ”yes” or ”no” but a number indicating probability of ”yes”. Basic courses: divide into ”discrete” and ”continuous”, and are mainly restricted to ”finite” or ”short term” problems involving a finite number of events or random variables. To escape these bounds: measure theory (introduced to probability by Kolmogorov). Unify discrete/continuous, and enable the study of long term or limiting properties. Ironically, many theorems will be about how randomness disappears or is constrained in the limit.
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تاریخ انتشار 2012