Streszczenie
A notion of entropy of a normal state on a finite von Neumann algebra in
Segal’s sense is considered, and its superadditivity is proven together with a necessary and
sufficient condition for its additivity. Bounds on the entropy of the state after measurement
are obtained, and it is shown that a weakly repeatable measurement gives minimal entropy
and that a minimal state entropy measurement satisfying some natural additional conditions
is repeatable.