Principles of mathematical analysis

By W. Rudin. 1964

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In Pure Mathematics

Citations in the corpus

A Tight and Unified Analysis of Extragradient for a Whole Spectrum of Differentiable Games (2019, methodology): “By the inverse function theorem (see for instance Rudin (1976)), ω 7→ ω + ηv ( ω ) is invertible in a neighborhood of ω ∗ and its inverse, which is P η , is continuously differentiable there.”
Normalizing Flows for Probabilistic Modeling and Inference (2019, background): “Imitation learning Schroecker et al. (2019) use normalizing flows within the imitationlearning paradigm for control problems.”
Toeplitz and Circulant Matrices: A Review (2005, methodology): “The primary goal of this work is to prove a special case of Szegö’s asymptotic eigenvalue distribution theorem in Theorem 9.”
Design and Stability of Load-Side Primary Frequency Control in Power Systems (2013, background): “By the inverse function theorem [32], can be written as a continuously differentiable function of , denoted by , with”
Assouad Dimension and Fractal Geometry (2020, background): “Some of my favourite introductory books on analysis include: Howie [138], Rudin [244] and Stewart-Tall [257].”
Multidimensional Stochastic Processes as Rough Paths: Theory and Applications (2010, unknown): “[143] or [134].”
Mutual information and minimum mean-square error in Gaussian channels (2004, background): “where (76) is due to Lemmas 2 and 4. Note that the order of expectation with respect to PX and the derivative with respect to the SNR can be exchanged as long as the input has finite power by Lebesgue’s (Dominated) Convergence Theorem [45], [ 46 ] (see also Lemma 8 in Appendix IV).”
Semi-Implicit Variational Inference (2018, background): “…rewrite it as the limit of a double sequence S(K,J), where K,J ∈ {1, 2, . . . , }, and check the condition for the interchange of iterated limits (Rudin, 1964; Habil, 2016): i) The double limit exists; ii) Fixing one index of the double sequence, the one side limit exists for the other index…”