Measuring Sets: Finite vs. Countably Infinite

[zeebo17]

I just started learning some basic measure theory.

Could someone explain the difference between $$\overline{F(A \times A)}$$ and $$\overline{F(A) \times F(A)}$$ where A is a finite set. Also, how would this be different in A was an countably infinite set?

Thanks!

 

[g_edgar]

where A is a finite set.

It is nice you told us what A is. But you didn't say what F and the bar are.