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The integral defined in this book extends the integral of the usual abstract theory. Every function integrable according to the old definition is still integrable according to the new definition, and has the same integral, but there are more integrable functions. All important properties of the integral remain intact, and some new ones even appear.
KeywordsIntegration Theory Vector Lattice Banach Lattice Lebesgue Dominate Convergence Theorem Complete Vector Lattice
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