Abstract
We introduce a new class of multivariate functions H Λ p (I d ), which includes some classical sets of functions such as isotropic and anisotropic Sobolev and Holder-Nikolskii as special cases or as a subclass in the sense of continuous imbedding. Then we prove that when p > 1 the e-complexity of the integration problem in the randomized setting as well as in the average case setting is significantly smaller than that in the worst case deterministic setting.
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