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.
