Real Analysis and Probability: Measurability: Borel Isomorphism and Analytic Sets

By R. M. Dudley. 2002

2,447 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Minimax Estimation of Kernel Mean Embeddings (2016, methodology): “Moreover it is well known (Dudley, 2002, Theorem 9.4.4) that ψ̃z ∈ Cb(R d) as ψ̃z is the characteristic function of Tz.”
Infinite-Horizon Policy-Gradient Estimation (2001, background): “(For definitions see, for example,(Dudley, 1989).)”
Optimal Rates for the Regularized Least-Squares Algorithm (2007, neutral): “2 of [12].”
On the geometry of metric measure spaces. II (2006, methodology): “For further reading we recommend [16], [29], [45], [55] and [56].”
A Few Notes on Statistical Learning Theory (2002, background): “One can turn to [5] for a more detailed introduction, or to [34, 8] for a complete and rigorous analysis.”
Functional clustering and identifying substructures of longitudinal data (2007, unknown): “Proof of theorem 1 Since {ρ.d/l , l 1} is an orthonormal basis of the FPC subspace in cluster d, by Parseval’s identity (e.g. Ash (1972)), ‖Ỹ .c/c −μ.d/‖2 =ΣMdl=1 |〈Ỹ .c/c −μ.d/, ρ.d/l 〉|2 if and only if Ỹ .c/c −μ.d/ ∈S .d/Md .”
Approximation of Haar distributed matrices and limiting distributions of eigenvalues of Jacobi ensembles (2009, background): “We also prove that the empirical distribution of the (complex) eigenvalues of a Jacobi ensemble converges to the circular law.”
Conformally invariant scaling limits: an overview and a collection of problems (2006, background): “Since that Hausdorff space is compact, the space of Borel probability measures on it is compact with respect to weak convergence of measures [26].”
Randomly Forced Nonlinear Pdes and Statistical Hydrodynamics in 2 Space Dimensions (2006, unknown): “This is the assertion of the celebrated Kantorovich Theorem, see [KA77] and [Dud89].”
Optimal transportation, topology and uniqueness (2010, background): “255 of [40] or Theorem I-55 of [103].”
Compositions of random transpositions (2004, methodology): “t ≥ cn there is a coupling of the sequence of transpositions Tj and a PD(1) sample Y such that P h Y − X(π t)/|Vt G| ∞ < ǫ i > 1 − ǫ. 2 Weak convergence has several equivalent formulations (see [Dud89]), and we have opted to use the coupling version here. The PD(1) distribution is a probabilit”