Extention of Lebesgue measure

Question

For $n \in \Bbb N$, can we extend the Lebesgue measure to some measure(or complete measure) on $\Bbb R^n$? Can we extent the Lebesgue measure to some measure on the power set of $\Bbb R^n$? (The answer is negative for $n=3$, by using Banach- Tarski s paradox) Many thanks for your help.