Banach Space/Examples/Square-Integrable Real-Valued Mappings

Example of Banach Space

Let $S$ be the space of all square-integrable real-valued functions.

Then $S$ is a Banach space.

Proof

This theorem requires a proof. In particular: First we need to defined what a square-integrable function is. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Banach space
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Banach space