Axiomatic probability
Perhaps you noticed in the last post that I couldn’t help myself from slipping in just a little probability, when imagining throwing a dart at the number line. That shows how probability theory can be helpful in thinking about measures. What about the other way round: why is it useful to view probability theory as a sub-branch of measure theory?Suppose we have a uniform random variable: a random number, between zero and 1, equally likely to be anywhere on the number line. How likely is it to be
- between 0 and 1/2?
- exactly equal to 2/3?
- between 1/6 and 1/3, if I’ve told you it’s between 0 and 1/2?
