Reconstruction of the One-Dimensional Lebesgue Measure
نویسندگان
چکیده
منابع مشابه
Singular Spectrum of Lebesgue Measure Zero for One-dimensional Quasicrystals
The spectrum of one-dimensional discrete Schrödinger operators associated to strictly ergodic dynamical systems is shown to coincide with the set of zeros of the Lyapunov exponent if and only if the Lyapunov exponent exists uniformly. This is used to obtain Cantor spectrum of zero Lebesgue measure for all aperiodic subshifts with uniform positive weights. This covers, in particular, all aperiod...
متن کاملLebesgue measure in the infinite - dimensional space ?
We consider the sigma-finite measures in the space of vector-valued distributions on the manifold X with characteristic functional
متن کاملLebesgue 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 کاملInstitute for Mathematical Physics Does There Exist the Lebesgue Measure in the Infinite-dimensional Space? Does There Exist the Lebesgue Measure in the Infinite-dimensional Space?
We consider the sigma-finite measures in the space of vector-valued distributions on the manifold X with characteristic functional
متن کاملRandomness – 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 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: Formalized Mathematics
سال: 2020
ISSN: 1898-9934,1426-2630
DOI: 10.2478/forma-2020-0008