The Pettis integral is a generalization of the Lebesgue integral that is used to integrate functions taking values in Banach spaces, rather than just in the real or complex numbers. It is particularly significant when dealing with vector-valued functions and weakly measurable functions. In more formal terms, let \( X \) be a Banach space, and let \( \mu \) be a measure on a measurable space \( (S, \Sigma) \).
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