Boole inequality

Let $(\\Omega,\\mathcal{F},P)$ be a probability space and $\\{A_{1},A_{2},\\cdots\\}$ be a sequence of eventssuch that $\\{A_{1},A_{2},\\cdots\\}\\subset\\mathcal{F}$ . Then

P(\\bigcup_{n=1}^{\\infty}A_{n})\\leq\\sum_{n=1}^{\\infty}P(A_{n}).

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