منابع مشابه
Splitting Necklaces and Measurable Colorings of the Real Line
A (continuous) necklace is simply an interval of the real line colored measurably with some number of colors. A well-known application of the Borsuk-Ulam theorem asserts that every k-colored necklace can be fairly split by at most k cuts (from the resulting pieces one can form two collections, each capturing the same measure of every color). Here we prove that for every k ≥ 1 there is a measura...
متن کاملPartitions of the Plane into Sets Having Positive Measure in Every Non-null Measurable Product Set
1 . Introduction . The following question was posed by D . Maharam : Can one divide the unit square into two or more measurable sets each of which has a non-null intersection with every product set A XB of positive measure, where A and B are subsets of the unit interval? In this paper we construct a class of such partitions of the plane, including some that retain the property under various tra...
متن کاملWhen is the ring of real measurable functions a hereditary ring?
Let $M(X, mathcal{A}, mu)$ be the ring of real-valued measurable functions on a measure space $(X, mathcal{A}, mu)$. In this paper, we characterize the maximal ideals in the rings of real measurable functions and as a consequence, we determine when $M(X, mathcal{A}, mu)$ is a hereditary ring.
متن کاملInformation and entropy of countable measurable partitions. I
In ergodic theory, the notions of information and entropy are separated from each other. In the existing literature, it is usual to assume the additive nature of information. In this paper, we have proposed a general definition of information in § 2 and studied its properties extensively in § 3. In § 4, information and entropy of countable measurable partitions of a Lebesgue probability space h...
متن کاملOn Realization of Björner's 'continuous Partition Lattice' by Measurable Partitions
Björner [1] showed how a construction by von Neumann of examples of continuous geometries can be adapted to construct a continuous analogue of finite partition lattices. Björner's construction realizes the continuous partition lattice abstractly, as a completion of a direct limit of finite lattices. Here we give an alternative construction realizing a continuous partition lattice concretely as ...
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: Advances in Mathematics
سال: 1973
ISSN: 0001-8708
DOI: 10.1016/0001-8708(73)90105-9