The monotone convergence theorem is any of a number of related theorems proving the good convergence behaviour of monotonic sequences. |
| Теорема Леви о монотонной сходимости |  |
Теорема о монотонной сходимости — это теорема из теории интегрирования Лебега, имеющая фундаментальное значение для функционального анализа и теории вероятностей, где служит инструментом для доказательства многих положений. Википедия
6 окт. 2015 г. · The Monotone Convergence Theorem (MCT), the Dominated Convergence Theorem (DCT), and Fatou's Lemma are three major results in the theory of Lebesgue ... |
1) If {an} is non-decreasing and bounded above, then {an} converges to L = lub{an}. 2) If {an} is non-decreasing and unbounded, then {an} diverges to. ∞. |
The monotone convergence theorem states that if a sequence increases and is bounded above by a supremum, it will converge to the supremum. |
Definitions: • We say {an} is monotonically (monotone) increasing if ∀n, an+1 ≥ an. • We say {an} is monotonically (monotone) decreasing if ∀n, an+1 ≤ an. • A ... |
5 сент. 2021 г. · If {an} is increasing and bounded above, then it is convergent. · If {an} is decreasing and bounded below, then it is convergent. |
Videolar 18 сент. 2014 г. · The Monotone Convergence Theorem says if the sequence is increasing and bounded above or decreasing and bounded below, then the sequence converges to a limit. |
[PDF] 1. Monotone Sequence Theorem - CDN cpb-us-e2.wpmucdn.com › dist › files › 2020/04 › Lecture-10
20 апр. 2020 г. · Monotone Sequence Theorem: (sn) is increasing and bounded above, then (sn) converges. Note: The same proof works if (sn) is nondecreasing (sn+1 ... |
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