Abstract
An entity called “outer measure” defined on all subsets of a set but fulfilling only some of the desiderata of Remark 1.1.6. Extraction of a measure from it via the “Caratheodory condition”. Lebesgue outer measure and Lebesgue measure on the real line. Lebesgue integrability of every Riemann integrable function. A set having no Lebesgue measure (“nonmeasurable” set of real numbers). Induced measure and integral on a subset. Lebesgue integral over [0, \( {\mathbb{R}} \)) and improper integral of Riemann type.
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