An elementary introduction to modern convex geometry, in flavors of geometry

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Query Strategies for Evading Convex-Inducing Classifiers (2010, background): “This volume (and thus the integral) can be bounded by enclosing the cap within a hypersphere; cf. Ball (1997).”
Satisfying Real-world Goals with Dataset Constraints (2016, methodology): “This is the Brunn-Minkowski inequality [e.g. Ball, 1997].”
Introduction to the non-asymptotic analysis of random matrices (2010, background): “choice of the subjects. Concentration of measure and its applications to random matrix theory are only brieﬂy mentioned. For an introduction into concentration of measure suitable for a beginner, see [9] and [49, Chapter 14]; for a thorough exposition see [56, 43]; for connections with random matric”
On the Margin Theory of Feedforward Neural Networks (2018, background): “Thus, we have Now the statement follows by Lemma 2.3 of (Ball, 1997).”
On the Sensitivity of Adversarial Robustness to Input Data Distributions (2018, unknown): “Considering robust accuracy as the clean accuracy with a smaller gap between the spheres, the next theorem provides a theoretical guarantee in relating together the difﬁculty of attaining good accuracy under attack and the model capacity (Ball, 1997), verifying our intuition above.”