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Examples ofbounded function
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Compare this with aboundedfunction, for which the constant does not depend on "x".
From
This example is from Wikipedia and may be reused under a CC BY-SA license.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Since the empty set has measure 0, one can believe that everyboundedfunctionis essentially bounded.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Aboundedfunctionis basically a function that is unbounded on the empty set (which is not mathematically precise but gives the basic idea).
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.By contrast, the characteristic function always exists (because it is the integral of aboundedfunction on a space of finite measure), and thus may be used instead.
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Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Rather, a bounded linear operator is a locallyboundedfunction.
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Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.The essential range of an essentiallyboundedfunction"f" is always compact.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.The set of all bounded functions defined on 0, 1 is much bigger than the set of continuous functions on that interval.
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Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.If we consider a family of bounded functions, this constant can vary across functions in the family.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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