theory, the Borel–Cantelli lemma is a theorem about sequences of events. In general, it is a result in measure theory. It is named after Émile Borel and Francesco...

\infty }\mathbb {P} \left(A_{n}\right).} In probability, the two Borel–Cantelli lemmas can be useful for showing that the limsup of a sequence of events...

lemma Borel's law of large numbers Borel measure Borel–Kolmogorov paradox Borel–Cantelli lemma Borel–Carathéodory theorem Heine–Borel theorem Borel determinacy...

Fundamental lemma of sieve theory Borel–Cantelli lemma Doob–Dynkin lemma Itô's lemma (stochastic calculus) Lovász local lemma Stein's lemma Wald's lemma Glivenko–Cantelli...

prefix of one of these strings. Both follow easily from the second Borel–Cantelli lemma. For the second theorem, let Ek be the event that the kth string...

{ X n = 1 } {\displaystyle \{X_{n}=1\}} are independent, second Borel Cantelli Lemma ensures that P ( lim sup n { X n = 1 } ) = 1 {\displaystyle P(\limsup...

probability theory. Cantelli's later work was all on probability theory. Borel–Cantelli lemma, Cantelli's inequality and the Glivenko–Cantelli theorem are result...

Glivenko–Cantelli theorem (sometimes referred to as the Fundamental Theorem of Statistics), named after Valery Ivanovich Glivenko and Francesco Paolo Cantelli...

{\displaystyle \sum _{n=1}^{\infty }\Pr(A_{n})<\infty ,} then the Borel-Cantelli Lemma implies the result. So let us estimate Pr ( A n ) {\displaystyle...

Elementary event "Almost surely" Independence (probability theory) The Borel–Cantelli lemmas and Kolmogorov's zero–one law Conditional probability Conditioning...

Circumplanetary disk – Accumulation of matter around a planet Second Borel–Cantelli Lemma, If ∑ n = 1 ∞ Pr ( E n ) = ∞ {\displaystyle \sum _{n=1}^{\infty }\Pr(E_{n})=\infty...

probability but not almost surely. This can be verified using the Borel–Cantelli lemmas. X n   → p   X ⇒ X n   → d   X , {\displaystyle X_{n}\ {\xrightarrow...

limit of certain probabilities must be 0 or 1. It may refer to: Borel–Cantelli lemma Blumenthal's zero–one law for Markov processes, Engelbert–Schmidt...

primes predicts incorrectly that it has limit 1 when λ≥2 (using the Borel–Cantelli lemma). Maier proved his theorem using Buchstab's equivalent for the counting...

measure Borel regular measure Radon measure Measurable function Null set, negligible set Almost everywhere, conull set Lp space Borel–Cantelli lemma Lebesgue's...

Kolmogorov's two-series theorem Random field Conditional random field Borel–Cantelli lemma Wick product Conditioning (probability) Conditional expectation Conditional...

stopping Galton–Watson processes Resource Dependent Branching Processes Borel–Cantelli lemma Robbins' problem (of optimal stopping) Pascal processes BRS-inequality...

single-sample technique Bootstrapping (statistics) Bootstrapping populations Borel–Cantelli lemma Bose–Mesner algebra Box–Behnken design Box–Cox distribution Box–Cox...

The concept of a normal number was introduced by Émile Borel (1909). Using the Borel–Cantelli lemma, he proved that almost all real numbers are normal, establishing...

subject to certain assumptions, so must some elementary particles. Borel–Cantelli lemma Princeton Philosophy Department bio "Simon Bernard Kochen". Office...

converges with probability 1 2 {\displaystyle {\frac {1}{2}}} . Borel–Cantelli lemma Hewitt–Savage zero–one law Lévy's zero–one law Tail sigma-algebra...

probability theory, similar to Kolmogorov's zero–one law and the Borel–Cantelli lemma, that specifies that a certain type of event will either almost surely...

non-positive almost surely by setting α = nβ for any β > 1 and applying the Borel–Cantelli lemma. Show that liminf and limsup of − 1 n log ⁡ j ( n , X ) {\displaystyle...

used to induce the topology on set X. Using the discrete metric The Borel–Cantelli lemma is an example application of these constructs. Using either the discrete...

approximations implies divergence of the series follows from the Borel–Cantelli lemma. The converse implication is the crux of the conjecture. There have...

Chung, K. L.; Erdös, P. (1952-01-01). "On the application of the Borel–Cantelli lemma". Transactions of the American Mathematical Society. 72 (1): 179–186...

irrationality measure at least 2. On the other hand, an application of Borel-Cantelli lemma shows that almost all numbers have an irrationality measure equal...

Borel algebra, measure, set, space, summation, Borel's lemma, paradox – Émile Borel Borel–Cantelli lemma – Émile Borel and Francesco Paolo Cantelli Borel–Carathéodory...

the classical strong law of large numbers in the direction of the Borel–Cantelli lemma. The idea of such a result is probably due to Robbins, but the method...

mathematician – Borel algebra, Borel's lemma, Borel's law of large numbers, Borel measure, Borel–Kolmogorov paradox, Borel–Cantelli lemma, Borel–Carathéodory...