The Lebesgue Integral

Let {X,A,μ} be a measure space and E ∈ A. For a function \(f:E \to {{\mathbb{R}}^{*}}\) and c∈ℝ, set $$\left[ {f > c} \right] = \left\{ {x \in E\left| {f\left( x \right) > c} \right.} \right\}.$$ (1.1)