Let gamma be a simple closed curve in R ^ 2. Is the bounded component of the complement of gamma always Lebesgue measurable?
(If you're wondering why I consider my question lazy, the answer is that it's arguable that I should have spent more time googling for the answer before posting. My first few attempts to find the answer this way have failed. I believe that this question has been asked by more than 16.3 people and that it's therefore googlable.)