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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. 5}

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\textbf{1.} 
Prove the uniqueness of the Borel measure.


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\textbf{2.}
Compute $\displaystyle\int_0^1 f(x) \dcobound x$, where $f(x) = 10$ if $x$ 
belongs to the Cantor set, and on any interval thrown away in the construction
process of the Cantor set, the graph of $f$ is the upper semicircle built 
on this interval as a diameter.



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