Why we need sigma and integration
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Why we need sigma ?
By forming a sigma-algebra, we have formed a sort of safe haven for our measures to operate within, while also allowing us to make reasonable manipulations to get what we want, such as taking unions and complements.
Why we need integration ?
Along with differentiation, integration is a fundamental operation of calculus, and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others.
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