probability theory - In the Proof of Kolmogorov's Strong Law of

I understand everything in this proof concerning the strong law of large numbers, except for the line highlighted in red. I do not understand why $$\frac{X_1 + +X_n}{n}$$ is measurable with res

Law of Large Numbers Strong and weak, with proofs and exercises

Law of large numbers - Wikipedia

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Law of Large Numbers Strong and weak, with proofs and exercises

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Law of large numbers - Wikipedia

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Law of Large Numbers Strong and weak, with proofs and exercises