Titlebook: Measure and Category; A Survey of the Anal John C. Oxtoby Textbook 19711st edition Springer-Verlag New York 1971 calculus

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Lebesgue Measure in ,-Space,of the notion of volume to a larger class of sets. Thus Lebesgue measure has a different meaning in spaces of different dimension. However, since we shall usually regard the dimension as fixed, there is no need to indicate . explicitly in our notations.

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The Property of Baire,when these operations are taken to define addition and multiplication, respectively. Such a class is also closed under the operations of union and difference. It is therefore a ring of subsets of its union, as this term was defined in Chapter 3.

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,The Poincaré Recurrence Theorem,oint of view, this “recurrence theorem” has a special interest, because in proving it Poincaré anticipated the notions of both measure and category. Publication of his treatise, “Les méthodes nouvelles de la mécanique céleste” [29], antedated slightly the introduction of either notion.

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