Hyperfinite factors are a special type of von Neumann algebra that can be approximated by finite-dimensional algebras. They are defined as factors that are isomorphic to the weak operator closure of the algebra of bounded operators on a separable Hilbert space, and they play an important role in understanding the structure of von Neumann algebras and their classification. The unique properties of hyperfinite factors make them crucial for discussions around Murray-von Neumann equivalence, particularly in how they relate to the notion of being 'finite' in this context.
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