Construction
The discussion that follows parallels the most common expository approach to the Lebesgue integral. In this approach, the theory of integration has two distinct parts:
- A theory of measurable sets and measures on these sets.
- A theory of measurable functions and integrals on these functions.
The function whose integral is to be found is then approximated by certain so-called simple functions, whose integrals can be written in terms of the measure. The integral of the original function is then the limit of the integral of the simple functions.
Read more about this topic: Lebesgue Integration
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