Infinite Dimensional Analysis: A Hitchhiker’s Guide

By Charalambos D. Aliprantis, Kim C. Border. 1994

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Citations in the corpus

Fair Regression: Quantitative Definitions and Reduction-based Algorithms (2019, background): “Since f ( X ) is a real-valued random variable under Borel σ -algebra, it is fully characterized by its cumulative distribution function, and so it sufﬁces to consider sets S = [0 , z ] for z ∈ [0 , 1] (see, e.g., Theorem 10.49 of Aliprantis & Border, 2006). service (cf. Buolamwini & Gebru, 2018).”
Probabilistic Voting in the Spatial Model of Elections: The Theory of Office-motivated Candidates (2005, background): “Suppose (xA, x ∗ B) is an equilibrium but xA does not maximize (1), so there exists x ′ ∈ X such that ∑”
Minimax Theorem for Latent Games or: How I Learned to Stop Worrying about Mixed-Nash and Love Neural Nets (2020, unknown): “From (Aliprantis and Border, 2006, Chap.”
Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities (2014, background): “52 in Aliprantis and Border (2006) the function (x, p) 7→ m(x, θ∗(p)) is jointly measurable and hence so is p 7→ E[m(Xi, θ∗(p))].”
Performative Prediction (2020, background): “θPO ∈ argmin θ∈[0,1] E Z∼D(θ) ( Y −θX − 1 2 )2 ⇐⇒ θPO = μ 1− 2ε .”
The numéraire portfolio in semimartingale financial models (2007, background): “17 of [2]; for shorter proofs of the specific results, see [28].”
Measurability of semimartingale characteristics with respect to the probability law (2013, unknown): “We omit the details.”
Hierarchies of Belief and Interim Rationalizability (2004, background): “To see that this is valid, recall that by Uryshon’s Metrization Theorem (see Aliprantis and Border (1994)), any Polish action space can be embedded in the Hilbert cube H = [0, 1]N.”