Non-measurable sets and the equation $f(x+y)=f(x)+f(y)$
نویسندگان
چکیده
منابع مشابه
NON-MEASURABLE SETS AND THE EQUATION fix+y)=fix)+fiy)
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 ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1951
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1951-0040387-4