Griebel, M.M.GriebelOswald, P.P.Oswald2022-03-052022-03-052017https://publica.fraunhofer.de/handle/publica/24835410.1016/j.jco.2017.01.003We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings. The construction has been used in an exemplary way for guiding dimension- and scale-adaptive algorithms in application areas such as statistical learning theory, reduced order modeling, and information-based complexity. We prove results on compact embeddings, norm equivalences, and the estimation of ε(lunate)-dimensions. A new condition for the equivalence of weighted ANOVA and anchored norms is also given.en510journal article