NON-MEASURABLE SETS AND THE EQUATION fix + y ) = fix ) + fiy )

  title={NON-MEASURABLE SETS AND THE EQUATION fix + y ) = fix ) + fiy )},
  author={Israel Halperin},
1. A set of S real numbers which has inner measure m*(S) different from its outer measure m*iS) is non-measurable. An extreme form, which we shall call saturated non-measurability, occurs when ra*(S)=0 but m*iSM)=miM) for every measurable set M, miM) denoting the measure of M. This is equivalent to: both S and its complement have zero inner measure. More generally, if a fixed set B of positive measure is under consideration, a subset S of B will be called s-non-mble. if both 5 and its… CONTINUE READING