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I'm not quite sure what you're talking about, but in measure theory there's a well-known approach where you start with a commutative algebra A equipped with a linear operator ∫: A -> k, where k is your ground field (like the real numbers or complex numbers), obeying some stuff.
This is why I love maths twitter.. we’re forced to condense rigorous mathematical definitions into the essential bits, leaving behind little golden nuggets of intuition that are otherwise hard to come by
