2 papers
math.FA2023
Bochner integrals and neural networks
Paul C. Kainen, A. Vogt
A Bochner integral formula is derived that represents a function in terms of weights and a parametrized family of functions. Comparison is made to pointwise formulations, norm ineq…
math.PR2012
The Mean: Axiomatics, Generalizations,Applications
John E. Gray, Andrew Vogt
We present an axiomatic approach to the mean and discuss generalizations of the mean, including one due to Kolmogorov based on the Weak Law of Large Numbers. We offer examples and…