Algebraic structures are fundamental mathematical entities defined by sets equipped with operations that satisfy specific axioms, such as groups, rings, and fields. Function spaces, by contrast, are ...

We characterize the compact and weakly compact weighted composition operators on the Banach space Cp(T, X) of those continuous functions from a completely regular Hausdorff space T into a Banach space ...

We prove that a probability measure over a space of functions induces a measure over the product space of the image and range of these functions. As an application, we show that the equilibrium of ...

Back in 2013, a handful of researchers at Google set loose a neural network on a corpus of three million words taken from Google News texts. The neural net’s goal was to look for patterns in the way ...