sums and products of simple functions are simple functions

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Theorem

Scalar multiples, linear combinations, and products of simple functions are also simple functions.

Proof

This can be seen by checking that the resulting functions are measurable and that their ranges are finite.

References

References

See Also

Mentions

Mentions

File Last Modified
Functional Analysis Lecture 10 2025-07-14

Created 2025-07-14 Last Modified 2025-07-14