  Quantum Measurement problem studied in Information Theory approach of systems
selfdescription which exploits the information acquisition incompleteness for
the arbitrary information system. The studied model of measuring system (MS)
consist of measured state S environment E and observer $O$ processing input S
signal.
  $O$ considered as the quantum object which interaction with S,E obeys to
Schrodinger equation (SE). MS incomplete or restricted states for $O$ derived
by the algebraic QM formalism which exploits Segal and $C^*$-algebras. From
Segal theorem for systems subalgebras it's shown that such restricted states
$V^O=|O_j> < O_j|$ describes the classical random 'pointer' outcomes $O_j$
observed by $O$ in the individual events. The 'preferred' basis $|O_j>$ defined
by $O$ state decoherence via $O$ - E interactions.
