Real and complex analysis

By W. Rudin. 1968

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Fast Two-Sample Testing with Analytic Representations of Probability Measures (2015, methodology): “By Fubini’s theorem we get Use of Fubini’s theorem is justiﬁed, since the iterated integral is ﬁnite [23][Theorem 8.8 b] i.e.”
On Convergence of Emphatic Temporal-Difference Learning (2015, positive): “Therefore, by a theorem on integration (Rudin, 1966, Theorem 1.38, p. 28-29), we can define a measurable function ψ on (S ×A)∞ such that the following hold: (i) on a set D2 ⊂ (S ×A)∞ with PX(D2) = 1, ψ(x) = ∞∑ k=0 ( λ(s−k) i(s−k) + (1− λ(s−k)) f(x(−k)) ) · φ(s−k) · ( β(s−k, a−k, s−k+1) · · ·β(s−1,…”
Relaxation of signed integral functionals in BV (2009, background): “Standard references on these topics include [7,12,16,18, 37 ,41], on which most of the presentation is based.”
Adjoints of linear fractional composition operators on the Dirichlet space (2003, background): “The corresponding result for H2( ) is a theorem of Paley and Wiener (see [12], p.”