Riemann integral from Lebesgue framework
Abstract
This work analyzes the relationship between the Riemann and Lebesgue integrals, showing how measure theory allows for a simplification of the proofs of properties of the Riemann integral. In particular, it is shown that the interchange of limits and integrals, which in the Riemann framework requires additional hypotheses and technical arguments, arises naturally through Lebesgue’s Dominated Convergence Theorem. This approach highlights the Lebesgue integral as a more general and conceptual framework for the study of convergence and integrability of functions.
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