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Absolute Extrema. Consider the function f(x) = x2 + 1 over the interval ( − ∞, ∞). As x → ± ∞, f(x) → ∞. Therefore, the function does not have a largest value. However, since x2 + 1 ≥ 1 for all real numbers x and x2 + 1 = 1 when x = 0, the function has a smallest value, 1, when x = 0.

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About. Transcript. The Extreme value theorem states that if a function is continuous on a closed interval [a,b], then the function must have a maximum and a minimum on the …

Extreme Value Theory offers a careful, coherent exposition of the subject starting from the probabilistic and mathematical foundations and proceeding to the statistical theory. The book covers both the classical one-dimensional case as well as finite- and infinite-dimensional settings. All the main topics at the heart of the subject are introduced in a systematic …

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