Probability and Measure

By P. Billingsley. 1980

How researchers see this paper

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

Estimation and Inference of Heterogeneous Treatment Effects using Random Forests (2015, methodology): “One way to do so is using the Lindeberg central limit theorem [e.g., Billingsley, 2008].”
Gaussian Process Behaviour in Wide Deep Neural Networks (2018, background): “n Section 2.2 that with a countable index set convergence with respect to the metric ˆis equivalent to convergence of each nite-dimensional marginal. The Cramer-Wold device (Cramer and Wold, 1936) (Billingsley, 1986, p. 383) states that convergence of a sequence of nite-dimensional vectors to some l”
Less hashing, same performance: Building a better Bloom filter (2006, background): “The Count-Min sketch consists of an array Count of width w e/ and depth d ln 1/δ : Count[1, 1], .”
Multilayer feedforward networks are universal approximators (1989, background): “Functions that are not Bore1 measurable exist (e.g., Billingsley, 1979, pp. 36-37) but they are pathological.”