On connection between the double and the iterated integrals (in Ukrainian)

Let $f \colon [0,1]^2 \to \mathbb{R}$ be a Riemann integrable
function on $[0,1]^2$. Denote $f(x,y) = f^x(y) = f_y(x)$ and $X_{\overline{R}}(f) = \{ x \in [0,1] : f^x \; \mbox{is not Riemann integrable}\}$, $Y_{\overline{R}}(f) = \{ y \in [0,1] : f_y \; \mbox{is not Riemann integrable}\}$.
It is proved that for such a function $f$ the sets $X_{\overline{R}}(f)$ and $Y_{\overline{R}}(f)$ are subsets of $F_\sigma$--sets which have the Lebesgue measure zero. And conversely, if we have two sets $A$ and $B$ which are subsets of $F_\sigma$--sets of zero Lebesgue measure then there exists a Riemann integrable function $f \colon [0,1]^2 \to \mathbb{R}$ with $X_{\overline{R}}(f)=A$, $Y_{\overline{R}}(f)=B$.