If our statistical tests show that it is somehow "unlikely" that these consequences hold, then we can conclude that it is also "unlikely" that our statistical model for $A$ and $B$ is correct. In particular, using theoretical considerations, we can know with "absolute" certainty, if an assumption is actually correct, what consequences must necessarily follow from that assumption. So (according to my rudimentary understanding of statistics) we employ statistical models to try to model $A$ and $B$ as random variables, and we use statistical tests to see how much those statistical models "make sense". In other words we do not know exactly how to consider them as random variables even if we knew with certainty that they were random variables, so the definition given above doesn't necessarily make sense without a lot of interpretation (since the definition requires us to consider $A$ and $B$ as random variables, which we don't necessarily know how to do "in the best way"). The statistics comes in because we do not have perfect knowledge of the universe, so we do not know exactly whether $A$ and $B$ "really are" random variables, and even if we did, we do not have perfect enough knowledge of $A$ and $B$ to say with absolute certainly whether the above formula does or does not hold. (Of course we have to use multiplication instead of addition, since probabilities are bounded between $0$ and $1$ inclusive, and multiplication of such numbers is closed under multiplication but not addition.) I.e., $A$ and $B$ together are "just the sum of their parts" and are "not greater than the sum of their parts". In other words, there is no interaction between $A$ and $B$ which we need to take into consideration when trying to deduce "information about $A$ and $B$ considered together" from "information about $A$ alone" and "information about $B$ alone". The (un)equation basically says that "information about $A$ and $B$ considered together" is not completely determined by "information about $A$ alone" and "information about $B$ alone". I would say (from a purely mathematical perspective) that, considering both $A$ and $B$ are random variables, variable $A$ influences variable $B$ if and only if they are not independent, i.e.
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