Isometrically invariant extensions of Lebesgue measure

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Numerical Modeling of Toroidal Dynamical Systems with Invariant Lebesgue Measure

Computer simulat ions of dynamical systems can cont ain bot h discretizations, in which finite machine arithmet ic replaces cont inuum state spaces , and realizations , in which a continuous syste m is replaced by some approximation such as a computational method. In some circumstances, complicated theoret ical behavior collapses to t rivial and degenerate behavior. In others, the computation m...

متن کامل

Lebesgue Measure

How do we measure the ”size” of a set in IR? Let’s start with the simplest ones: intervals. Obviously, the natural candidate for a measure of an interval is its length, which is used frequently in differentiation and integration. For any bounded interval I (open, closed, half-open) with endpoints a and b (a ≤ b), the length of I is defined by `(I) = b − a. Of course, the length of any unbounded...

متن کامل

Subsets of the Plane with Small Linear Sections and Invariant Extensions of the Two-dimensional Lebesgue Measure

We consider some subsets of the Euclidean plane R2, having small linear sections (in all directions), and investigate those sets from the point of view of measurability with respect to certain invariant extensions of the classical Lebesgue measure on R2. Many examples of paradoxical sets in a finite-dimensional Euclidean space, having small sections by hyperplanes in this space, are known in th...

متن کامل

Randomness – beyond Lebesgue Measure

Much of the recent research on algorithmic randomness has focused on randomness for Lebesgue measure. While, from a computability theoretic point of view, the picture remains unchanged if one passes to arbitrary computable measures, interesting phenomena occur if one studies the the set of reals which are random for an arbitrary (continuous) probability measure or a generalized Hausdorff measur...

متن کامل

Bounded Archiving using the Lebesgue Measure

Many modern multiobjective evolutionary algorithms (MOEAs) store the points discovered during optimization in an external archive, separate from the main population, as a source of innovation and/or for presentation at the end of a run. Maintaining a bound on the size of the archive may be desirable or necessary for several reasons, but choosing which points to discard and which to keep in the ...

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

ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 1990

ISSN: 0002-9939

DOI: 10.1090/s0002-9939-1990-1027089-7