Null-Control and Measurable Sets

نویسندگان

  • Jone Apraiz
  • Luis Escauriaza
چکیده

We prove the interior and boundary null–controllability of some parabolic evolutions with controls acting over measurable sets.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

F U N D a M E N T a Mathematicae on Haar Null Sets

We prove that in Polish, abelian, non-locally-compact groups the family of Haar null sets of Christensen does not fulfil the countable chain condition, that is, there exists an uncountable family of pairwise disjoint universally measurable sets which are not Haar null. (Dougherty, answering an old question of Christensen, showed earlier that this was the case for some Polish, abelian, non-local...

متن کامل

Universally measurable sets in generic extensions

A subset of a topological space is said to be universally measurable if it is measured by the completion of each countably additive σ-finite Borel measure on the space, and universally null if it has measure zero for each such atomless measure. In 1908, Hausdorff proved that there exist universally null sets of real numbers of cardinality א1, and thus that there exist at least 2א1 such sets. La...

متن کامل

GENERALIZED FUZZY VALUED $theta$-Choquet INTEGRALS AND THEIR DOUBLE-NULL ASYMPTOTIC ADDITIVITY

The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...

متن کامل

Measurable Sensitivity

We introduce the notions of measurable and strong measurable sensitivity, which are measure-theoretic versions of the conditions of sensitive dependence on initial conditions and strong sensitive dependence on initial conditions, respectively. Strong measurable sensitivity is a consequence of light mixing, implies that a transformation has only finitely many eigenvalues, and does not exist in t...

متن کامل

Real Analysis Chapter 3 Solutions Jonathan Conder

2. Let E be measurable, and suppose that E is ν-null but |ν|(E) 6= 0. Then ν+(E) − ν−(E) = ν(E) = 0 and ν+(E) + ν−(E) = |ν|(E) > 0, so ν+(E) = ν−(E) > 0. Since ν+ ⊥ ν−, there exist disjoint measurable sets A and B covering X such that A is ν+-null and B is ν−-null. In particular ν+(E ∩ B) = ν+(E ∩ B) + ν+(E ∩ A) = ν+(E) > 0 but ν−(E∩B) ≤ ν−(B) = 0. This implies that ν(E∩B) > 0, which is a contr...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • CoRR

دوره abs/1107.4132  شماره 

صفحات  -

تاریخ انتشار 2011