Infinite sequences defined with a finite alphabet are studied and it is shown that the set of sequences with bounded run-length has measure zero with respect to the Borel measure.Such sequences arise in many applicati...Infinite sequences defined with a finite alphabet are studied and it is shown that the set of sequences with bounded run-length has measure zero with respect to the Borel measure.Such sequences arise in many applications including digitization of certain linear systems involving flows on the circle and 2-torus,large scale simulation,and cryptology.They are basic objects of study in ergodic theory.展开更多
In this paper,a necessary and sufficient condition of a measure to be the product Borel probability measure on the product space of some compact metric spaces are given.
In this note, we study the existence of an initial trace of nonnegative solutions for the following problem ut-div（｜▽um｜p-2^▽um）＋uq = 0 in QT = Ω × （0, T ）. We prove that the initial trace is an outer r...In this note, we study the existence of an initial trace of nonnegative solutions for the following problem ut-div（｜▽um｜p-2^▽um）＋uq = 0 in QT = Ω × （0, T ）. We prove that the initial trace is an outer regular Borel measure, which may not be locally bounded for some values of parameters p, q, and m. We also study the corresponding Cauchy problems with a given generalized Borel measure as initial data.展开更多
文摘Infinite sequences defined with a finite alphabet are studied and it is shown that the set of sequences with bounded run-length has measure zero with respect to the Borel measure.Such sequences arise in many applications including digitization of certain linear systems involving flows on the circle and 2-torus,large scale simulation,and cryptology.They are basic objects of study in ergodic theory.
基金Supported by the NSF of China(10571063)Supported by the NSF of Guangdong Province(05006515)
文摘In this paper,a necessary and sufficient condition of a measure to be the product Borel probability measure on the product space of some compact metric spaces are given.
文摘In this note, we study the existence of an initial trace of nonnegative solutions for the following problem ut-div（｜▽um｜p-2^▽um）＋uq = 0 in QT = Ω × （0, T ）. We prove that the initial trace is an outer regular Borel measure, which may not be locally bounded for some values of parameters p, q, and m. We also study the corresponding Cauchy problems with a given generalized Borel measure as initial data.
