Let $A, A' ⊂ 2 ^S$.
Prove that: If $A ⊂ A'$ , then $σ(A) ⊂ σ(A')$.
2026-03-26 07:58:44.1774511924
Proof of the statement based on measure theory.
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Hint:
Observe hat $\mathcal A\subseteq\mathcal A'\subseteq\sigma(\mathcal A')$ where $\sigma(\mathcal A')$ denotes a $\sigma$-algebra and then apply the definition of $\sigma(\mathcal A)$.