For fractional discrete nonautonomous p-Laplace equations driven by superlinear noise, we construct a pullback measure attractor in the space of all probability measures on Banach space \(l^p\) (which is larger than \(l^2\) ) for \(p>2\) . Using a so-called two-stage approach which is different from the recent ten references for other models in Hilbert spaces, we provide the estimates for exponential decay moments and tail moments in the Banach space, which lead to the pullback absorption and asymptotic tightness of the dual measure process. Moreover, we prove the upper semicontinuity of the enlarged measure attractors with respect to the noise intensity. It is the first time to study measure attractors when the underlying space is a Banach space.
