# Notes on: Arjovsky, M., Chintala, S., & Bottou, L\'eon (2017): Wasserstein Gan

## Table of Contents

## Notation

- parametric family of densities
- is real data examples
- denotes
*real*data distribution - denotes
*distribution*of the parametrized density - a compact metric space (e.g. space of images )
- denotes the set of all Borel sets of , i.e. forms a Borel sigma-algebra
- denotes the space of probability measures defined on
- is the
**total variation (TV)**distance - is a random variable with a fixed distribution
- is the parametric function (e.g. a neural network) which
*generates*samples following a certain distribution - is the weight space, i.e. , and is a compact set
**critic**refers to the , a Lipschitz-continuous function used in the Kantorovhich-Rubinstein duality to make the problem of minimzing Earth-Mover distance between and tractable**discriminator**refers to the in a "standard" GAN- with since is
*bounded* - is a
*normed vector space* with

*dual norm*- is the
*normed space*of the dual - is a
*signed measure*over