is R Lebesgue-measurable?

May 2010
7
1
Hi! I want to ask if is \(\displaystyle R^2\) is Lebesgue-measurable?
If yes why?
This is true also for R, R^3 and so on?
Are they Peano-Jordan measurable?

I thought they were because their complementar is empty. Sorry for my english. Thank you.
 
Aug 2009
228
80
Hi! I want to ask if is \(\displaystyle R^2\) is Lebesgue-measurable?
If yes why?
This is true also for R, R^3 and so on?
Are they Peano-Jordan measurable?

I thought they were because their complementar is empty. Sorry for my english. Thank you.
If you have a sigma algebra on any space it will contain the entire space. This holds for any sigma algebra so the whole space is always measurable.