# Harmonic Function Theory/Definitions, elementaries

**Definition (harmonic function)**:

A **harmonic function** is a function such that .^{[note 1]}

**Proposition (closure properties of harmonic functions)**:

Harmonic functions are closed under the following operations:

- Addition, subtraction
- Locally uniform convergence

## Footnotes edit

- ↑ The
**Laplace operator**is defined as .