# Accession Number:

## AD0256667

# Title:

## MEASURE PRESERVING FUNCTIONS ON LOCALLY COMPACT SPACES,

# Descriptive Note:

# Corporate Author:

## SYRACUSE UNIV N Y

# Personal Author(s):

# Report Date:

## 1961-04-01

# Pagination or Media Count:

## 12.0

# Abstract:

The following theorem is proved Let M and N be compact metric spaces with Borel measures u and v, respectively, such that every non-empty open set has positive measure. Let f M N be a continuous function having the property whenever both A and fA are Borel measurable, then uA vfA. Then there exists a subset F of M of the first category and of measure zero on which f is not one-to-one and such that f M - F is a homeomophism. This result without the continuity assumption is then generalized to locally compact metric spaces. The conclusion is slightly weaker. Some examples are given to prove that other likely extensions are false in general. Author