| 11. | Measurable functions don't naturally form a collection of morphisms, because they're not closed under composition.
|
| 12. | We start with the set of all measurable functions from to or which are bounded.
|
| 13. | Measurable sets, given in a measurable space by definition, lead to measurable functions and maps.
|
| 14. | In mathematics, particularly in measure theory, "'measurable functions "'are bijective and its inverse is also measurable.
|
| 15. | Call a real valued measurable function on a measure space simple if its range is finite.
|
| 16. | Where is any probability distribution and any-measurable function.
|
| 17. | Let B ( ? ) be the space of bounded ?-measurable functions, equipped with the uniform norm.
|
| 18. | Suppose is a measurable set and is a nondecreasing sequence of non-negative measurable functions on such that
|
| 19. | In the informal formulation of J . E . Littlewood, " every measurable function is nearly continuous ".
|
| 20. | *So long as there are non-measurable sets in a measure space, there are non-measurable functions from that space.
|
