| 1. | In particular, any locally integrable function has a distributional derivative.
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| 2. | For a given integrable function, consider the function defined by:
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| 3. | Locally integrable functions play a prominent role in functions of bounded variation.
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| 4. | Now we will show that a Darboux integrable function satisfies the first definition.
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| 5. | Suppose is an integrable and square-integrable function.
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| 6. | This includes the case of improperly Riemann integrable functions.
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| 7. | Before collapse, the wave function may be any square-integrable function.
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| 8. | Are given by convolution with integrable functions and have uniformly bounded operator norms.
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| 9. | He later constructed an example of an integrable function whose Fourier series diverges everywhere.
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| 10. | Let be a square-integrable function.
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