On the Construction of Independence Counterexamples
Bruce R. Johnson, Benjamin J. Tilly · The American Statistician · 1996
A simple method of modifying probability to create independence counterexamples is given. This method can be used to construct counterexamples for finite collections of events and for infinite sequences of events. It is shown how to construct examples of countable collections of events where all equations in the (countable) family of “product rules” that define independence are satisfied except for one or, more generally, except for an arbitrarily specified subfamily.