Abstract
This chapter contains descriptions of 7 great theorems published in the Annals of Mathematics in 2001.
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- 1.
For example, for \(d=3\) we are talking about the “usual” volume, for \(d=2\) about the covered area, while for \(d=1\), about the length of the covered interval.
- 2.
The term “moderate” comes from the fact that probabilities of the form \(\mathrm {P}(V_t \le f(t)\mathrm {E}[V_t])\) for some function f(t) such that \(\lim \limits _{t \rightarrow \infty } f(t) = 0\) are known as probabilities of large deviations.
- 3.
Namely, n! bijections. Indeed, f(1) can take n possible values, f(2) \(n-1\) values (all except f(1)), f(3) \(n-2\) values, and so on, so the total number of possible bijections f is \(n\cdot (n-1)\cdot (n-2)\cdots 1 = n!\)
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Grechuk, B. (2019). Theorems of 2001. In: Theorems of the 21st Century. Springer, Cham. https://doi.org/10.1007/978-3-030-19096-5_1
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DOI: https://doi.org/10.1007/978-3-030-19096-5_1
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