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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
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; C. Covering lemma; ... Vitali covering lemma; W. Whitney covering lemma This page was last edited on 1 January 2018, at 13:47 (UTC) ...
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 .
Borel's law of large numbers, named after Émile Borel, states that if an experiment is repeated a large number of times, independently under identical conditions, then the proportion of times that any specified event is expected to occur approximately equals the probability of the event's occurrence on any particular trial; the larger the ...
Second Borel–Cantelli lemma – Theorem in probability; Hilbert's paradox of the Grand Hotel – Thought experiment of infinite sets, another thought experiment involving infinity; Law of truly large numbers – Law of statistics; Murphy's law – Adage typically stated as: "Anything that can go wrong, will go wrong"
Borel–Cantelli 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 .