Let be a sequence of measurable sets in .Define and . Prove or disprove and . Can anyone help me to initialize the proof?
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Originally Posted by problem Let be a sequence of measurable sets in .Define and . Prove or disprove and . Can anyone help me to initialize the proof? A characteristic function can only take the values 0 or 1. Therefore for each x in X, must be 0 or 1. Then it's just a matter of definition-chasing: Therefore Similar argument for the liminf.
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