Smiling
Nov11-08, 12:42 AM
1. The problem statement, all variables and given/known data
We have two measures: miu and miu', with miu(E)=0 if E can be written as E' union E'' where the projection of E' onto the first coordinate is countable, and the projection of E'' onto the second coordinate is countable. If E cannot be written in this way, miu(E)=infinity.
Also, miu'(E)=0 if E can be written as E' union E'' union E''' where the projection of E' onto the first coordinate is countable, the projection of E'' onto the second coordinate is countable and the projection of E''' onto the line y=x is countable. If E cannot be written in this way, miu'(E)=infinity.
Now, let E={(x,-x)|x is in R}
Compute miu(E) and miu'(E)....
2. Relevant equations
3. The attempt at a solution
I need to show that miu(E)=infinity and that miu'(E)=0....
We have two measures: miu and miu', with miu(E)=0 if E can be written as E' union E'' where the projection of E' onto the first coordinate is countable, and the projection of E'' onto the second coordinate is countable. If E cannot be written in this way, miu(E)=infinity.
Also, miu'(E)=0 if E can be written as E' union E'' union E''' where the projection of E' onto the first coordinate is countable, the projection of E'' onto the second coordinate is countable and the projection of E''' onto the line y=x is countable. If E cannot be written in this way, miu'(E)=infinity.
Now, let E={(x,-x)|x is in R}
Compute miu(E) and miu'(E)....
2. Relevant equations
3. The attempt at a solution
I need to show that miu(E)=infinity and that miu'(E)=0....