The Lebesgue Integral

Having completed our study of Lebesgue measure, we are now ready to consider the Lebesgue integral. Before diving into the details of its construction, though, we would like to give a broad overview of the subject. Most of the propositions and theorems in these notes will not have proofs, though all of this will be proven later. Given a measure space (X,M, μ) and a function f : X → R, we wish to define the Lebesgue integral of f on X, denoted ∫