I didn't drive the car for three weeks. When I went to open the car to drive to work my keyless entry fob wouldn't work so I used the actual key to open the door. When I tried to start the car of course it wouldn't turn over, no lights or display popped up either. I took the plastic insert "key" out and tried to use my key but that didn't work either and now I can't even get the key out. What could be the problem?


Question: Lebesgue measure of any line in $\mathbb{R^2}$.
Answer: Without loss of generality  we can suppose that over line $l$ has the form $l=\mathbb R \times 0$. 

This follows from the translation- and rotation invariance of the lebesgue-measure.
(We can move our line such that it contains zero. Then we can rotate it)

We write $l=\cup_{k=0}^{\infty}([-k,k]\times 0)$

Now we obtain:

$\lambda_2(l)=\lambda_2(\cup_{k=0}^{\infty}([-k,k]\times 0))\leq\sum_{k=0}^{\infty}\lambda([-k,k]\times 0)=0 $