All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 88 Next

Displaying 1741 – 1760 of 3925

Showing per page

Measures of fuzziness and operations with fuzzy sets.

Siegfried Gottwald, Ernest Czogala, Witold Pedrycz (1982)

Stochastica

We discuss the effects that the usual set theoretic and arithmetic operations with fuzzy sets and fuzzy numbers have with respect to the energies and entropies of the fuzzy sets connected and of the resulting fuzzy sets, and we also compare the entropies and energies of the results of several of those operations.

Measures of maximal entropy for random β -expansions

Karma Dajani, Martijn de Vries (2005)

Journal of the European Mathematical Society

Let β > 1 be a non-integer. We consider β -expansions of the form ∑ i = 1 ∞ d i / β i , where the digits ( d i ) i ≥ 1 are generated by means of a Borel map K β defined on { 0 , 1 } ℕ × [ 0 , ⌊ β ⌋ / ( β − 1 ) ] . We show that K β has a unique mixing measure ν β of maximal entropy with marginal measure an infinite convolution of Bernoulli measures. Furthermore, under the measure ν β the digits ( d i ) i ≥ 1 form a uniform Bernoulli process. In case 1 has a finite greedy expansion with positive coefficients, the measure of maximal entropy is Markov. We also discuss the uniqueness of β -expansions....

Measures on compact HS spaces

Mirna Džamonja, Kenneth Kunen (1993)

Fundamenta Mathematicae

We construct two examples of a compact, 0-dimensional space which supports a Radon probability measure whose measure algebra is isomorphic to the measure algebra of 2 ω 1 . The first construction uses ♢ to produce an S-space with no convergent sequences in which every perfect set is a G δ . A space with these properties must be both hereditarily normal and hereditarily countably paracompact. The second space is constructed under CH and is both HS and HL.

Measures on Corson compact spaces

Kenneth Kunen, Jan van Mill (1995)

Fundamenta Mathematicae

We prove that the statement: "there is a Corson compact space with a non-separable Radon measure" is equivalent to a number of natural statements in set theory.

Measure-Theoretic Characterizations of Certain Topological Properties

David Buhagiar, Emmanuel Chetcuti, Anatolij Dvurečenskij (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

It is shown that Čech completeness, ultracompleteness and local compactness can be defined by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non-empty support. This shows that these three topological properties are measurable, similarly to the classical examples of compact spaces, pseudo-compact spaces and realcompact spaces.

Measure-theoretic unfriendly colorings

Clinton T. Conley (2014)

Fundamenta Mathematicae

We consider the problem of finding a measurable unfriendly partition of the vertex set of a locally finite Borel graph on standard probability space. After isolating a sufficient condition for the existence of such a partition, we show how it settles the dynamical analog of the problem (up to weak equivalence) for graphs induced by free, measure-preserving actions of groups with designated finite generating set. As a corollary, we obtain the existence of translation-invariant random unfriendly colorings...

Currently displaying 1741 – 1760 of 3925