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We consider the product of infinitely many copies of a spin-$1\over 2$system. We construct projection operators on the corresponding nonseparableHilbert space which measure whether the outcome of an infinite sequence of$\sigma^x$ measurements has any specified property. In many cases, productstates are eigenstates of the projections, and therefore the result ofmeasuring the property is determined. Thus we obtain a nonprobabilistic quantumanalogue to the law of large numbers, the randomness property, and all otherfamiliar almost-sure theorems of classical probability.Comment: 7 pages in LaTe

Using classical probability to guarantee properties of infinite quantum sequences