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