ON SOME PROPERTIES OF BOUNDED INTERNAL FUNCTIONS.
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1967
- Accession Number
- AD0653072
Entities
People
- R. F. Taylor
Organizations
- California Institute of Technology