[math] \newcommand{\mathds}{\mathbb}[/math]

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Given a commutative von Neumann algebra, written as

[[math]] A=L^\infty(X) [[/math]]

with [math]X[/math] being a measured space, write, by using the Gelfand theorem,

[[math]] A=C(\widehat{X}) [[/math]]

with [math]\widehat{X}[/math] being a compact space, and understand the correspondence [math]X\to\widehat{X}[/math].