(i) Show that non-void open sets in (mathbb{R}) (resp. (mathbb{R}^{n}) ) have always strictly positive Lebesgue measure....

Question:

(i) Show that non-void open sets in \(\mathbb{R}\) (resp. \(\mathbb{R}^{n}\) ) have always strictly positive Lebesgue measure.

[let \(U\) be open. Find a small ball in \(U\) and inscribe a square.]

(ii) Does your answer to part (i) hold also for closed sets?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question
Question Posted: