I've got the following problem to solve:

let λ be σ-additive 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 σ-additive 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?