In this article, we consider the random sampling in the image space
V$$ V $$ of an idempotent integral operator on mixed Lebesgue space
Lp,q()ℝn+1$$ {L}^{p,q}\left({\mathbb{R}}^{n+1}\right) $$. We assume some decay and regularity conditions on the integral kernel and show that the bounded functions in
V$$ V $$ can be approximated by an element in a finite‐dimensional subspace of
V$$ V $$ on
CR,S=[]−R2,R2n×[]−S2,S2$$ {C}_{R,S}={\left[-\frac{R}{2},\frac{R}{2}\right]}^n\times \left[-\frac{S}{2},\frac{S}{2}\right] $$. Consequently, we show that the set of bounded functions concentrated on
CR,S$$ {C}_{R,S} $$ is totally bounded and prove with an overwhelming probability that the random sample set uniformly distributed over
CR,S$$ {C}_{R,S} $$ is a stable set of sampling for the set of concentrated functions on
CR,S$$ {C}_{R,S} $$. Further, we propose an iterative scheme to reconstruct the concentrated functions from their random measurements.
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