  Under certain restrictions on $s,p,q$, the Triebel-Lizorkin spaces can be
viewed as generalised fractional Sobolev spaces $W^{s,p}_q$. In this article,
we show that the Bourgain-Brezis-Mironescu formula holds for
$W^{s,p}_q$-seminorms in arbitrary domain. This addresses an open question
raised by Brazke-Schikorra-Yung in [Bourgain-Brezis-Mironescu convergence via
Triebel-Lizorkin spaces; Calc. Var. Partial Differential Equations; 2023].
