Noncommutative integration refers to the generalization of the concept of integration to noncommutative spaces, where the order of multiplication matters, such as in operator algebras. This framework allows for the definition of integrals that behave differently from traditional calculus, accommodating the complexities inherent in quantum mechanics and noncommutative geometry. Through this approach, various constructs like noncommutative measures and differential forms can be explored, linking it to measure theory, differential geometry, and functional analysis.
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