I have started studying Lebesgue integration and I have a question regarding the Lebesgue integral:

In the wikipedia entry of "Lebesgue integration" they define the Lebesgue integral as:

Let be a positive real-valued function.

where . The Lebesgue integration notes that I am studying defines the Lebesgue integral of a positive measurable function as I want to know if this wiki definition is equivalent to the integral constructed from simple functions, if so how can this be easily shown?