# Distribution Theory/Distributions

## Preliminaries, convergence, TVSEdit

**Definition**:

A **distribution** is a linear and continuous map from to for an open .

**Construction**:

We now construct the LCTVS of distributions on , denoted by . Indeed, to induce the locally convex topology, we use a family of seminorms given by

- for ,

where ranges over the natural numbers and over all compact subsets of .

## Stability propertiesEdit

## Distributions and functionsEdit

## Operations on distributionsEdit

When given a distribution, we can do several things with it. These include: