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Measure Theory and Lebesgue Integration Theories
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As discussed in the previous chapter, the fundamental theories of measure and Lebesgue integration are the prerequisites for the formalization of probability theory in higher-order logic. The scope of this chapter is primarily the formalization of these foundations. Both formalizations of measure theory and Lebesgue integral (Mhamdi, Hasan, & Tahar, 2011), presented in this chapter, are based on the extended-real numbers. This allows us to define sigma-finite and even infinite measures and handle extended-real-valued measurable functions. It also allows us to verify the properties of the Lebesgue integral and its convergence theorems for arbitrary functions. Therefore, the chapter begins with a description of the formalization of extended real numbers.
Title: Measure Theory and Lebesgue Integration Theories
Description:
As discussed in the previous chapter, the fundamental theories of measure and Lebesgue integration are the prerequisites for the formalization of probability theory in higher-order logic.
The scope of this chapter is primarily the formalization of these foundations.
Both formalizations of measure theory and Lebesgue integral (Mhamdi, Hasan, & Tahar, 2011), presented in this chapter, are based on the extended-real numbers.
This allows us to define sigma-finite and even infinite measures and handle extended-real-valued measurable functions.
It also allows us to verify the properties of the Lebesgue integral and its convergence theorems for arbitrary functions.
Therefore, the chapter begins with a description of the formalization of extended real numbers.
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