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On convergent-in-area polynomials in the interval [0,1]

Take any finite or infinite polynomial which converges in area in the interval between [0,1].  We can define equivalence classes on such space by mapping them back to distinct probability distributions, such that each equivalence class with all its elements is a semigroup under a particular operation.  We can extend each semigroup into a group if we incorporate an identity element and inverses.  Now we've created fun to last for a lifetime!  I've included these ideas in version 20 of Compendium.

Part I v20

There is more to come, as we spawn mathematical objects of weirdness that can be related back or extend probability theory.

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