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Questions about the properties of vector spaces and linear transformations, including linear systems in general.
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Projection on a countable union of linear subspace
For any natural number $n$, $V_n$ denotes a closed linear subspace of a $L_2(m)$ space, which is an Hilbert Space, where $m$ denotes a finite measure. Moreover $(V_n)$ is increasing, that is $V_n$ is …