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\begin{document}

\title{
Exam for ``Measure Theory and Integration'' (TMAIN) \\ winter semester 2018/2019
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\section*{Questions set No. 4}

\bigskip

\textbf{1.} 
Give the definition of the Lebesgue integral, and formulate and prove its main 
properties.


\bigskip


\textbf{2.}
Is it true that the union of two $\sigma$-algebras is a $\sigma$-algebra?



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