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It is named after Émile Borel and Francesco Paolo Cantelli, who gave statement to the lemma in the first decades of the 20th century. [1] [2] A related result, sometimes called the second Borel–Cantelli lemma, is a partial converse of the first Borel–Cantelli lemma. The lemma states that, under certain conditions, an event will have ...
Burnside's lemma also known as the Cauchy–Frobenius lemma; Frattini's lemma (finite groups) Goursat's lemma; Mautner's lemma (representation theory) Ping-pong lemma (geometric group theory) Schreier's subgroup lemma; Schur's lemma (representation theory) Zassenhaus lemma
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This is a direct implication from the Borel–Cantelli lemma. If S n is a sum of n real independent random variables: = + + then S n converges almost surely if and only if S n converges in probability. The proof can be found in Page 126 (Theorem 5.3.4) of the book by Kai Lai Chung. [13]
Félix Édouard Justin Émile Borel (French:; 7 January 1871 – 3 February 1956) [1] was a French mathematician [2] and politician. As a mathematician, he was known for his founding work in the areas of measure theory and probability .
Download as PDF; Printable version; ... Borel–Cantelli lemma; C. Covering lemma; ... Whitney covering lemma This page was last edited on 1 January 2018, at 13:47 ...
Proofs of Borel's lemma can be found in many text books on analysis, including Golubitsky & Guillemin (1974) and Hörmander (1990), from which the proof below is taken. Note that it suffices to prove the result for a small interval I = (− ε , ε ), since if ψ ( t ) is a smooth bump function with compact support in (− ε , ε ) equal ...
Borel–Cantelli lemma, Blumenthal's zero–one law for Markov processes, Engelbert–Schmidt zero–one law for continuous, nondecreasing additive functionals of Brownian motion, Hewitt–Savage zero–one law for exchangeable sequences, Kolmogorov's zero–one law for the tail σ-algebra, Lévy's zero–one law, related to martingale convergence,