The Nonexistence of Universal Countably Additive Measures

Alexander Kharazishvili
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Alexander Kharazishvili: Tbilisi State University, Andrea Razmadze Mathematical Institute

Chapter Chapter 19 in Lectures on Real-valued Functions, 2025, pp 187-197 from Springer

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

Date: 2025
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DOI: 10.1007/978-3-031-95369-9_19

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