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Counterexample

Is this true?

Convergence in probability ⇒ almost sure convergence

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

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86 counterexamples are free — including most of the ones Part C leans on hardest.

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Limit assumed to exist

Reasoning with a limit before establishing there is one. limsup is not lim.

See real exam options built on this mistakeDrill statements like this
probabilityconvergence

Go deeper· Explained in full in Modes of convergence and the limit theorems· Asked in CSIR NET December 2025· From Limit Theorems and Markov Chains › Modes of convergence, WLLN, SLLN, CLT

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