The tensor product of an infinite number of von Neumann algebras, if done naively, is usually a ridiculously large non-separable algebra. Instead showed that one should choose a state on each of the von Neumann algebras, use this to define a state on the algebraic tensor product, which can be used to produce a Hilbert space and a (reasonably small) von Neumann algebra. studied the case where all the factors are finite matrix algebras; these factors are called Araki–Woods factors or ITPFI factors (ITPFI stands for "infinite tensor product of finite type I factors"). The type of the infinite tensor product can vary dramatically as the states are changed; for example, the infinite tensor product of an infinite number of type I2 factors can have any type depending on the choice of states. In particular found an uncountable family of non-isomorphic hyperfinite type IIIλ factors for 0 < λ < 1, called Powers factors, by taking an infinite tensor product of type I2 factors, each with the state given by: