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We have mentioned several times Cantor’s classical theorem which states that the strict inequality \(\displaystyle \mathrm {card}(E) > \mathrm {card}(\mathcal {P}(E)) \) holds true for an arbitrary set E (see Chap. 3 ). In particular, taking \(E = \mathbb {N}\) , we obtain the existence of uncountable sets.

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The Nonexistence of Universal Countably Additive Measures

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  • 发表日期：

    2025年

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  • Alexander Kharazishvili

摘要

We have mentioned several times Cantor’s classical theorem which states that the strict inequality \(\displaystyle \mathrm {card}(E) > \mathrm {card}(\mathcal {P}(E)) \) holds true for an arbitrary set E (see Chap. 3 ). In particular, taking \(E = \mathbb {N}\) , we obtain the existence of uncountable sets.