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The talk is devoted tothe problem of singularity of distributions with independent symbols of $F$-expansion. Such general expansions include $s$-adic expansion, continued fraction expansion, Lueroth, Sylvester, Engel expansions, the second Ostrogradsky expansion and Ostrogradsky-Sierpinski-Pierce expension of real numbers as  partial cases. We will show general results on normal properties of $F$-expansion and  conditions on singularity of probability measures with independent symbols of $F$-expansion. We also  show several examples which demonstrate how these results can be used to prove singularity of famous  classes of probability measures generated by  Sylvester, $Q^*$, the second Ostrogradskiy, Ostrogradskiy-Sierpinski-Pierce expansions of real numbers.