Abstract
We suppose that the reader is acquainted with basic measure theory. However the common presentation of measure theory uses the Axiom of Choice without any comment. To replace the use of Axiom of Choice by a Weak Axiom of Choice or to avoid it at all, we present some facts about measure on a topological space, a brief construction of Lebesgue measure and we prove some of its basic properties. In Section 4.3 we recall the definition of the Lebesgue integral and we prove the basic results related to it. Finally, Section 4.4 is devoted to a brief presentation of the results which we shall intensively use: the Fubini Theorem and the Ergodic Theorem.
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© 2011 Springer Basel AG
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Bukovský, L. (2011). Measure Theory. In: The Structure of the Real Line. Monografie Matematyczne, vol 71. Springer, Basel. https://doi.org/10.1007/978-3-0348-0006-8_4
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DOI: https://doi.org/10.1007/978-3-0348-0006-8_4
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Publisher Name: Springer, Basel
Print ISBN: 978-3-0348-0005-1
Online ISBN: 978-3-0348-0006-8
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