Selected chapters of the measure theory

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Department of Mathematics

Synopsis:

Basic properties of finetely additive and sigma-additive measures, classic results (the Radon-Nikodym theorem and the Carathéodory theorem), the extension of finately additive measures (the Horn-Tarski technique, the Banach limit method, some questions of the lifting, etc.), the Hammer-Sobczyk theorem.

Requirements:

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Study materials:

1. K. P. S. Bhaskara Rao, M. Bhaskara Rao: Theory of Charges, Academic Press, 1983

2. J.L. Doob: Measure Theory, Springer New York, 2012

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No time-table has been prepared for this course

The course is a part of the following study plans:

• Doctoral studies, daily studies (compulsory elective course)
• Doctoral studies, combined studies (compulsory elective course)
• Doctoral studies, structured daily studies (compulsory elective course)
• Doctoral studies, structured combined studies (compulsory elective course)