I'm would be interesting in any construction of a probability space with n events (n is given), where for every subset of these events, it is also given whether or not, the family is mutually independent. Does such a probability space always exist? Do you know some reference for that?

For instance, it is well known that this is possible for n=3 to find pairwise independent events that are not mutually independent.

remarks - All events should be non trivial - Of course independence for k events implies independence for any subfamily. I can imagine that it is the only constraint on the data.



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