Search results
Results From The WOW.Com Content Network
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) ...
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 .
How much does the test cost? The Galleri test — which isn’t covered by insurance — doesn’t come cheap. At $949 a pop, it’s out of the price range of most people.
Given a Borel measure μ on a metric space X such that μ(X) > 0 and μ(B(x, r)) ≤ r s holds for some constant s > 0 and for every ball B(x, r) in X, then the Hausdorff dimension dim Haus (X) ≥ s. A partial converse is provided by the Frostman lemma: [7] Lemma: Let A be a Borel subset of R n, and let s > 0. Then the following are equivalent:
For (,) a measurable space, a sequence μ n is said to converge setwise to a limit μ if = ()for every set .. Typical arrow notations are and .. For example, as a consequence of the Riemann–Lebesgue lemma, the sequence μ n of measures on the interval [−1, 1] given by μ n (dx) = (1 + sin(nx))dx converges setwise to Lebesgue measure, but it does not converge in total variation.