Let (left{A_{n}ight}_{n=1}^{infty}) be a sequence of monotonically increasing events from a (sigma) field (mathcal{F}) of subsets of

Question:

Let $\left\{A_{n}ight\}_{n=1}^{\infty}$ be a sequence of monotonically increasing events from a $\sigma$ field $\mathcal{F}$ of subsets of a sample space $\Omega$. Prove that the sequence $\left\{A_{n}^{\mathrm{c}}ight\}_{n=1}^{\infty}$ is a monotonically decreasing sequence of events from $\mathcal{F}$.

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