Let $(\Omega, \mathcal{A})$ be a measure space and $A\subset \mathcal{A}$. Show that $\sigma(A) = \sigma(\sigma(A))$.
Do we have to use that the minimal sigma algebra is the intersection of all sigma algebras containing A?
Let $(\Omega, \mathcal{A})$ be a measure space and $A\subset \mathcal{A}$. Show that $\sigma(A) = \sigma(\sigma(A))$.
Do we have to use that the minimal sigma algebra is the intersection of all sigma algebras containing A?