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The paper proves the Strong Law of Large Numbers for integral functionals ofrandom fields with unboundedly increasing covariances. The case of functionaldata and increasing domain asymptotics is studied. Conditions to guarantee thatthe Strong Law of Large Numbers holds true are provided. The consideredscenarios include wide classes of non-stationary random fields. The discussionabout application to weak and long-range dependent random fields and numericalexamples are given.

Strong Law of Large Numbers for Functionals of Random Fields With Unboundedly Increasing Covariances