 for all subsets \(A\) and \(B\) of \(X.\) This requirement for mixing can be relaxed a bit by allowing for  fluctuations.[9]  That is, instead of requiring that the cocktail reach a uniform state of being mixed, we now only require that it be mixed on average. In other words, we allow that bubbles of either scotch or water may crop up every now and then, but they do so in a way that these fluctuations average out as time tends towards infinity. This translates into mathematics in a straightforward way. The deviation from the ideally mixed state at some time \(n\) is \(\mu(T_n B \cap A) - \mu(B)\mu(A)\). The requirement that the average of these deviations vanishes inspires the notion of weak mixing. A system is weak mixing iff