10 papers
Uniform Approximation of Continuous Functions by Nontrivial Simple Functions
Yu-Lin Chou
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions bei…
An Intrinsic Treatment of Stochastic Linear Regression
Yu-Lin Chou
Linear regression is perhaps one of the most popular statistical concepts, which permeates almost every scientific field of study. Due to the technical simplicity and wide applicab…
On Almost Uniform Continuity of Borel Functions on Polish Metric Spaces
Yu-Lin Chou
We show that, on any given finite Borel measure space with the ambient space being a Polish metric space, every Borel real-valued function is almost a bounded, uniformly continuous…
Sensitive Random Variables are Dense in Every
Yu-Lin Chou
We show that, for every and for every Borel probability measure over , every element of $L^{p}(\mathbb{R}, \mathscr{B}_{\mathbb{R}}, \…
Change of Measures for Spectral Stochastic Integrals
Yu-Lin Chou
Under mild conditions, it is possible to obtain, from almost purely measure-theoretic considerations and without any specific reference to stochastic processes, a change-of-measure…
A Remark on Lebesgue Criterion
Yu-Lin Chou
We remark a variant of the existence part of the fundamental theorem of calculus, which, together with the Lebesgue differentiation theorem, constitute a new proof that every Riema…