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Let R be the set of real numbers, and define R ∞ = ∞ i=1 R. We construct a complete measure space (R ∞ , L, λ) where the σ-algebra L contains the Borel subsets of R ∞ , and λ is a translation-invariant measure such that where m is Lebesgue measure on R. The measure λ is not σfinite. We prove three Fubini theorems, namely, the Fubini theorem, the mean Fubini-Jensen theorem, and the pointwise Fubini-Jensen theorem. Finally, as an application of the measure λ, we construct, via selfadjointdoi:10.2307/2048779 fatcat:d4lodmla3fgh5er74cvlg4aana