Abstract
Outer measure of subsets of \( {\mathbb{R}} \) as a generalisation of the length of an interval, its restriction to measurable subsets (Lebesgue measure) countable additivity and translation invariance, relation between measurability and openness, measurable functions, measurability of continuous and of monotone functions, generalisation to higher dimensions; approximation by simple functions; theorems of Egorov and Luzin.
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Shirali, S., Vasudeva, H.L. (2019). Measure in Euclidean Space. In: Measure and Integration. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-18747-7_2
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DOI: https://doi.org/10.1007/978-3-030-18747-7_2
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