Originally Posted by

**detalosi** @HallsofIvy, I appreciate your reply and I see my grammatical error. Being a new and very young student of Measure Theory (and mathematics in general) I have taken the advice of E. T. Bell to heart ("obvious" is the most dangerous word in mathematics). Below I have rewritten my question. Maybe you, Plato or someone else could shed some light on the matter.

@Plato, essentially what I would like to show is the following: If $\displaystyle \mathcal{G}$ is a $\displaystyle \sigma$-algebra then $\displaystyle \mathcal{G}=\sigma(\mathcal{G})$