Convergence in probability implies almost sure convergence
Is this true?
No — it is false.
Others that fail the same way
- Convergence in probability ⇒ almost sure convergence
- Uncorrelated ⇒ independent
- Pairwise independent events are mutually independent
- Every random variable has a moment generating function
- A mixture of two distributions is a linear combination of the variables
- The maximum of independent exponentials is exponential
From Limit Theorems and Markov Chains › Modes of convergence, WLLN, SLLN, CLT