I would like to know what should I verifiy in order to show that two probabilities are equal.
Here is the exercice :
Let $F_0$ be an algebra of sets over $\Omega$ and $P$, $P'$ two probabilities over $\sigma(F_0)$ (the $\sigma$-algebra generated by $F_0$).
Show that if $P=P'$ over $F_0$, then $P=P'$.
Should I show that $P(x\in A) = P'(x\in A)$ for all $A\in \Omega$ by double inclusion ? Or that these $A$ have the same mesure in $\Omega$ and $\sigma(F_0)$ ?