probability - Condition for strong law of large numbers : Understanding the solution - Mathematics Stack Exchange

I am reading the solution of the following task: Here is the solution: From where does the last inequality in the second line comes from? Everything else is totally clear to me.

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Introduction To Probability

Financial Modeling: A Clean, Short and Simple Statistical Point of View, by Pierre Blanchart

Why would the law of large numbers work if every event is completely independent? - Quora

Introduction To Probability: 9781886529236: Bertsekas, Dimitri P., Tsitsiklis, John N.: Books

probability theory - In the Proof of Kolmogorov's Strong Law of Large Numbers - Mathematics Stack Exchange

probability - Weak law vs strong law of large numbers - intuition - Cross Validated

Laws of Large Numbers (detailed explanation), by Anirudh G

Solved The Strong Law of Large Numbers states that Xˉ→E[X]

Solved (a) State and prove the weak law of large number. (b)

Probability: For the Enthusiastic Beginner: 9781523318674: Morin, David J.: Books