  When Alice and Bob have different quantum knowledges or state assignments
(density operators) for one and the same specific individual system, then the
problems of compatibility and pooling arise. The so-called first
Brun-Finkelstein-Mermin (BFM) condition for compatibility is reobtained in
terms of possessed or sharp (i. e., probability one) properties. The second BFM
condition is shown to be generally invalid in an infinite-dimensional state
space. An argument leading to a procedure of improvement of one state
assifnment on account of the other and vice versa is presented.
