Let θ ∈ (0, 1), λ ∈ [0, 1) and p, p0, p1 ∈ (1, ∞] be such that (1 − θ)/p0 +
θ/p1 = 1/p, and let ϕ, ϕ0, ϕ1 be some admissible functions such that ϕ, ϕp/p 0 0 and ϕp/p 1 1
are equivalent. We first prove that, via the ± interpolation method, the interpolation
hLp ϕ0 0),λ(X ), Lp ϕ1 1),λ(X ), θi of two generalized grand Morrey spaces on a quasi-metric measure
space X is the generalized grand Morrey space Lp ϕ),λ(X ). Then, by using block functions,
we also find a predual space of the generalized grand Morrey space. These results are new
even for generalized grand Lebesgue spaces.

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• INTERPOLATION AND DUALITY OF GENERALIZED GRAND MORREY SPACES ON QUASI-METRIC MEASURE SPACES