Let A ⊂ R be a measurable and bounded and l 1 ( A )...

Jameson Lucero

Jameson Lucero

Answered

2022-07-08

Let A R be a measurable and bounded and l 1 ( A ) > 0. Show that there exist a , b A that a b is irrational number.

Answer & Explanation

gozaderaradiox5

gozaderaradiox5

Expert

2022-07-09Added 19 answers

Suppose not. Fix some a 0 A. Then by our supposition, a 0 a is rational for every a A. In other words, A { q a 0 : q Q }. But the latter is countable

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