| 1. | The indicator function of any open set is lower semicontinuous.
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| 2. | The indicator function of a closed set is upper semicontinuous.
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| 3. | Where I _ C is the indicator function of the set C.
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| 4. | (This is the Cesaro limit of the indicator functions.
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| 5. | Involving indicator functions of the sets and their complements with respect to.
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| 6. | The indicator function is also known as the characteristic function.
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| 7. | Note that every simple function can be expressed as the linear combination of indicator functions.
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| 8. | Where is the indicator function of.
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| 9. | Formally, a simple function is a finite linear combination of indicator functions of measurable sets.
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| 10. | As suggested by the previous example, the indicator function is a useful notational device in combinatorics.
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