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  2. Borel–Cantelli lemma - Wikipedia

    en.wikipedia.org/wiki/BorelCantelli_lemma

    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 BorelCantelli lemma, is a partial converse of the first BorelCantelli lemma. The lemma states that, under certain conditions, an event will have ...

  3. Convergence of random variables - Wikipedia

    en.wikipedia.org/wiki/Convergence_of_random...

    This is a direct implication from the BorelCantelli 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]

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  5. List of lemmas - Wikipedia

    en.wikipedia.org/wiki/List_of_lemmas

    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

  6. Borel's lemma - Wikipedia

    en.wikipedia.org/wiki/Borel's_lemma

    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 ...

  7. Category:Covering lemmas - Wikipedia

    en.wikipedia.org/wiki/Category:Covering_lemmas

    BorelCantelli lemma; C. Covering lemma; ... Vitali covering lemma; W. Whitney covering lemma This page was last edited on 1 January 2018, at 13:47 (UTC) ...

  8. Émile Borel - Wikipedia

    en.wikipedia.org/wiki/Émile_Borel

    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 .

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