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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. 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

  4. 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 ...

  5. 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) ...

  6. Francesco Paolo Cantelli - Wikipedia

    en.wikipedia.org/wiki/Francesco_Paolo_Cantelli

    BorelCantelli lemma, Cantelli's inequality and the Glivenko–Cantelli theorem are result of his work in this field. In 1916–1917 he made contributions to the theory of stochastic convergence . In 1923 he resigned his actuarial position when he was appointed professor of actuarial mathematics at the University of Catania .

  7. Martingale (probability theory) - Wikipedia

    en.wikipedia.org/wiki/Martingale_(probability...

    In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values.

  8. Proofs of convergence of random variables - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_convergence_of...

    Proof: We will prove this statement using the portmanteau lemma, part A. First we want to show that (X n, c) converges in distribution to (X, c). By the portmanteau lemma this will be true if we can show that E[f(X n, c)] → E[f(X, c)] for any bounded continuous function f(x, y). So let f be such arbitrary bounded continuous function.

  9. List of nuclear weapons tests of India - Wikipedia

    en.wikipedia.org/wiki/List_of_nuclear_weapons...

    India's nuclear test series consists of a pair of series: Pokhran I and Pokhran II. Pokhran I was a single nuclear test conducted in 1974.