# Distribution Theory/Distributions

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## Contents

## Preliminaries, convergence, TVS[edit]

**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 properties[edit]

## Distributions and functions[edit]

## Operations on distributions[edit]

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