ON SOME PROPERTIES OF BOUNDED INTERNAL FUNCTIONS.
CALIFORNIA INST OF TECH PASADENA DEPT OF MATHEMATICS
Pagination or Media Count:
Let R be the real number system and let R be an ultrapower of R which is an enlargement of R. If omega is an infinitely large natural number, then the following bounded internal functions sin x omega, x epsilon R are considered. It is shown that the function f sub omega x sin omega x, x epsilon R is either sin ax for some a or is unmeasurable. Arithmetical conditions for omega are given in order that f sub omega is not measurable. It is also shown that there exists an infinitely large natural number omega such that sin omega x does not equal 0 but f sub omega identically equals 0. An application to integration theory is given.
- Theoretical Mathematics