| 41. | *Any non-constant function can be made non-measurable by equipping the domain and range with appropriate \ sigma-algebras.
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| 42. | A constant function is also considered linear in this context, as it is a polynomial of degree zero or is the zero polynomial.
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| 43. | Follows from the corresponding identity for the Lie bracket of vector fields, but this is true only up to a locally constant function.
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| 44. | A polynomial with a degree of 0 is simply a constant function; with a degree of 1 is a cubic, and so on.
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| 45. | For instance, if L ( x ) is the constant function, then we have a power law that holds for all values of x.
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| 46. | The function y ( x ) = 2 or just y = 2 is the specific constant function where the output value is c = 2.
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| 47. | This theorem is a significant strengthening of Liouville's theorem which states that the image of an entire non-constant function must be unbounded.
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| 48. | This use of " constant " as an abbreviation of " constant function " must be distinguished from the normal meaning of the word in mathematics.
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| 49. | Four days ago I edited the en . wikipedia constant function adding the definition in the introduction and all of section 1 and my own image.
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| 50. | Then f is not Lebesgue measurable and thus not integrable, but | f | \ equiv 1 / 2 is a constant function and clearly integrable.
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