
hahn decomposition
I've got the following problem to solve:
let λ be σadditive set function defined in the algebra m of subsets of X. Suppose that f:X > R is measurable and the integral int_X (f)dλ exists, k(a) = int_A (f)dλ (A ∈ m) is σadditive set function.
Find Hanh decomposition of X with respect to function k.
Is there any universal workflow of determining such decomposition. What should I pay attention to?

Re: hahn decomposition
Quote:
Universal Workflow
Alas, no Royal Road to Geometry.
$\displaystyle P=\{f\geq 0\}, N=\{f\leq 0\}$