Is it correct to define the F-measure as the harmonic mean of specificity and sensitivity in such a way? It is common to define the F-measure as a function of precision and recall, as mentioned in [1]:


  $F_{\beta}=\frac{(1+\beta^2)PR}{\beta^2 P+R}$


However I came across some other cases, another definition is used [2] (without weights):


  $F = H(sensitivity, 1- specificity)$


Where H is harmonic mean.

Reference:


F - measure derivation (harmonic mean of precision and recall)
https://link.springer.com/chapter/10.1007/978-3-540-68947-8_133.
https://stackoverflow.com/a/52892413/2243842
Yes, as they are effectively synonyms of one another. See for instance this link

If you pay attention, the first formula is the (weighted) harmonic mean of the recall and precision.