**Moderator: Please move my thread to the correct section. Sorry about posting it in the wrong location**(adsbygoogle = window.adsbygoogle || []).push({});

http://press.princeton.edu/chapters/s8008.pdf

In example 2 on page 11 of the text I linked above, the book uses the monotonicity property of the outer measure to conclude

##m_*(Q) \le |Q|## where Q is a cube.

However, in example 4 on the next page they require a more complicated argument to reach the conclusion

##m_*(R) \le |R|## where R is a rectangle.

My question is, why couldn't they use monotonicity again?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Real Analysis-Monotonicity

**Physics Forums | Science Articles, Homework Help, Discussion**