Question: Hello, I have real analysis questions. I need your help. Thank you so much. 10 Show that the set of real numbers that have a

Hello, I have real analysis questions.

I need your help.

Thank you so much.

Hello, I have real analysis questions. I need

10 Show that the set of real numbers that have a decimal expansion with the digit 5 appearing infinitely often is a Borel set.30 Show that lim 2k 1 if x is rational, lim cos (j!ntx) ) = 0 if x is irrational for every x E R. [This example is due to Henri Lebesgue. ]

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