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    $\begingroup$ Do you know where I can read about the mathematically rigorous definition of the very first integral expansion in your answer (if $|x\rangle$ had some finite representation as a column vector I would interpret this as an ordinary componentwise integral, however, since this is not the case there is probably some other definition to this)? $\endgroup$
    – Richard
    Commented Sep 28, 2022 at 21:23