-----Original Message----- From: math-fun-bounces+andy.latto=pobox.com@mailman.xmission.com [mailto:math-fun-bounces+andy.latto=pobox.com@mailman.xmission.com]On Behalf Of Thomas Colthurst Sent: Sunday, April 17, 2005 11:16 AM To: dasimov@earthlink.net; math-fun Subject: Re: [math-fun] Density question
David Wilson wrote:
Can someone give me an example of a set of density 1/2 on every interval of the real numbers?
Take [0,1/2), and then for every point x in it, flip a coin. If the coin is heads, keep x as is. If the coin is tails, replace x with x+1/2. Then shift the resulting set by all the integers.
That doesn't work. A set has S density 1/2 on [0,1] if the measure of S intersect [0,1] is 1/2. The set you describe is nonmeasurable (with probability 1). Andy Latto andy.latto@pobox.com