On non-measurable sets and invariant tori
نویسندگان
چکیده
منابع مشابه
On invariant sets topology
In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...
متن کاملMeasure zero sets with non - measurable sum
For any C ⊆ R there is a subset A ⊆ C such that A + A has inner measure zero and outer measure the same as C + C. Also, there is a subset A of the Cantor middle third set such that A+A is Bernstein in [0, 2]. On the other hand there is a perfect set C such that C + C is an interval I and there is no subset A ⊆ C with A + A Bernstein in I.
متن کاملNON-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 ...
متن کاملNull-Control and Measurable Sets
We prove the interior and boundary null–controllability of some parabolic evolutions with controls acting over measurable sets.
متن کاملMeasure zero sets whose algebraic sum is non - measurable
In this note we will show that for every natural number n > 0 there exists an S ⊂ [0, 1] such that its n-th algebraic sum nS = S + · · ·+ S is a nowhere dense measure zero set, but its n+1-st algebraic sum nS+S is neither measurable nor it has the Baire property. In addition, the set S will be also a Hamel base, that is, a linear base of R over Q. We use the standard notation as in [2]. Thus sy...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Chaos, Solitons & Fractals
سال: 2002
ISSN: 0960-0779
DOI: 10.1016/s0960-0779(01)00115-1