Mel Bochner - Alchetron, The Free Social Encyclopedia
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Lecture 12: Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence Theorem | Introduction to Functional Analysis | Mathematics | MIT OpenCourseWare
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Ilyas on Instagram: "those who snow Lebesgue? @statcsmemes The equation provided, \forall \phi \in B^*, \ \phi(\mathbf{E}[f]) = \int_{X} \phi(f(x)) \, d\mu(x), is a fundamental identity in Functional Analysis and Probability Theory that characterizes the Bochner integral \mathbf{E}[f] of a vector-valued function f. Here, f is a function mapping from a measure space (X, \mathcal{M}, \mu) to a Banach space B, and \mathbf{E}[f] is the Bochner integral (or expected value) of f, which is an element o
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