To study the analog of Suita'fs conjecture for domains ⊂Cn, n ≥ 2, Blocki introduced the invariant Fκ D (z) = KD(z)λIκ D(z), where KD (z) is the Bergman kernel of D along the diagonal and λIκ D(z) is the Lebesgue measure of the Kobayashi indicatrix at the point z. In this note, we study the behaviour of Fκ D (z) (and other similar invariants using different metrics) on strongly pseudconvex domains and also compute its limiting behaviour explicitly at certain points of decoupled egg domains in C2. © 2019 American Mathematical Society.