**A. Kharazishvili, A. Kirtadze**

## On the Measurability of Functions
with Respect to Certain Classes of Measures

**Abstract:**

The concept of measurability of real-valued functions with respect to various
classes of measures is introduced and the associated notion

of an absolutely nonmeasurable function is investigated. A characterization of
such functions is given. Also, it is shown that functions produced by the
classical Vitali partition of the real line are measurable with respect to the
class of all extensions of the Lebesgue measure on this line.

**Keywords:**

Absolutely nonmeasurable function, generalized Luzin set, Vitali partition,
extension of measure.

**MSC 2000:** 28A05, 28D05