Recent content by rs123

To be more clear about why I can't make sense of your example, surely your measure function `\mu(x) is the largest integer less than or equal to x' doesn't obey the countable additivity requirement \mu\left(\cup_{i\in\Omega}A_i\right)=\sum_{i\in \Omega}\mu(A_i)\;\;\forall A_i\cap A_j=\emptyset...

Let's forget intervals for now, that was just to make the two distinct with notation; I understand that it is is for measurable sets allowing the discussion of your example or the Dirichlet function or what have you: this surely is a result of being able to consider it as a sum over intervals in...

Hi all, Sorry if this is in the wrong place. I'm trying to understand probability theory a bit more rigorously and so am coming up against things like lebesgue integration and measure theory etc and have a couple of points I haven't quite got my head around. So starting from the basics...

Hi all, Apologies if this is stupid question, but I have the following situation. Given two measures u(x) and v(x) if u(x) is absolutely continuous to v(x) ( u<<v) I have a result such that \int_A f(x)dv(x) always takes the value \int_B g(x)du(x) But strictly \int_B g(x)du(x)\neq\int_A...