Abstract
Before revamping Riemann’s theory of integration with all its intuitive appeal one would try, of course, to prove limit theorems better than the Dominated Uniform Convergence Theorem I.6.5. One might imagine that the next result was discovered this way. It is an extremely modest result, applying as it does only to a sequence of step functions whose pointwise and monotone limit is a priori known to be a step function again. Yet the whole development of the Lebesgue integral rests on it.
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References
Bourbaki, N. Intégration, Hermann, Paris, 1965.
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© 1998 Birkhäuser Verlag
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Bichteler, K. (1998). Extension of the Integral. In: Integration - A Functional Approach. Modern Birkhäuser Classics. Springer, Basel. https://doi.org/10.1007/978-3-0348-0055-6_2
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DOI: https://doi.org/10.1007/978-3-0348-0055-6_2
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