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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Ensuring the measure condition $\mu(E) = \lambda$ in a lemma: need some clarification regard...

If $\mu(E)\geq\lambda$ you can choose a subset $E'$ with $\mu(E')>\lambda$. The following exhaustion argument ensures you can have an $E$ with $\mu(E)>\lambda$. Do as you said and get an $E$. If $\mu( …
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