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Probabilistic methods prove existence results in a nonconstructive fashion, by showing the chance of randomly selecting a solution is greater than zero.

2 votes

Theorems like the Lovász Local Lemma?

Does exchangeability qualify as a "relaxed form of independence"? There are a number of results for exchangeable sequences, for example Hong & Lee for a Weak Law of Large Numbers or Fortini, Ladelli & …
Robin Ryder's user avatar