Manuscript En05-C@1 · En05-C.tex · definition · aa213ea6

Definition: Conditional expectation

Conditional expectations are optional · lines 777–785

A conditional expectation onto $A \subseteq M$ is a UCP map $E : M \to A$ that fixes $A$ pointwise and satisfies

E (a_{1} x a_{2}) = a_{1} E (x) a_{2} (a_{1}, a_{2} \in A, x \in M) .

When convenient, its inclusion into $M$ is understood.

Displayed formulas in this passage

unlabeled · line 780
$E (a_{1} x a_{2}) = a_{1} E (x) a_{2} (a_{1}, a_{2} \in A, x \in M) .$