Borel–Cantelli lemmas
Theorem taught in Probability spaces and events, part of Stochastic processes
Borel–Cantelli lemmas
| Type | Theorem |
| Taught in | Probability spaces and events |
| Part | Stochastic processes |
| Questions using it | 1 |
If \sum_n\mathrm{P}(A_n)<\infty, then \mathrm{P}(A_n\text{ infinitely often})=0. If the events A_n are independent and \sum_n\mathrm{P}(A_n)=\infty, then \mathrm{P}(A_n\text{ infinitely often})=1.
Used in
- Taught in Probability spaces and events, where the derivation and examples are.
- Also used in Expectation and convergence
- Questions that use it (1) — Two series of events
- All 3 questions on Probability spaces and events