# is R Lebesgue-measurable?

• May 29th 2010, 04:23 AM
venturozzaccio
is R Lebesgue-measurable?
Hi! I want to ask if is $R^2$ 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.
• May 30th 2010, 01:46 AM
Focus
Quote:

Originally Posted by venturozzaccio
Hi! I want to ask if is $R^2$ 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.