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

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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