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For any Darboux function      f : [ 0 , 1 ] →  R f:\left [ {0,1} \right ] \to {\mathbf {R}}       and any      0 &gt; δ  &gt; 1 0 &gt; \delta &gt; 1       there is a point      x ∈  [ 0 , 1 −  δ  ] x \in \left [ {0,1 - \delta } \right ]       and a sequence      x n {x_n}       such that (a)      x n ∈  [ x + δ  n + 1 , x + δ  n ] ( n = 1 , 2 , …  ) {x_n} \in \left [ {x + {\delta ^{n + 1}},x + {\delta ^n}} \right ]\left ( {n = 1,2, \ldots } \right )       and (b)     ∑  n = 2 ∞  | f ( x n ) −  f ( x n −  1 ) | &gt; + ∞  \sum \nolimits _{n = 2}^\infty {\left | {f\left ( {{x_n}} \right ) - f\left ( {{x_{n - 1}}} \right )} \right |} &gt; + \infty      . Consequently, for every      f ∈  C [ 0 , 1 ] f \in C\left [ {0,1} \right ]       there is an absolutely continuous function      g g       such that      { x : f ( x ) = g ( x ) } \left \{ {x:f\left ( x \right ) = g\left ( x \right )} \right \}       is not bilaterally strongly porous.

For every continuous 𝑓 there is an absolutely continuous 𝑔 such that [𝑓=𝑔] is not bilaterally strongly porous