How do I show that the linear span of idempotents is dense in $L^{\infty}(\Omega,\mu)$ where $(\Omega,\mu)$ is a measure space? I don't really have any idea how to do this. Does it involve approximating some other class that is dense, say the simple functions?
2026-03-30 08:58:28.1774861108
Density of linear span of idempotents in $L^{\infty}$
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The simple functions are precisely the linear span of the idempotents.