Invariant measures and homogeneous uncountable universal graphs
نویسندگان
چکیده
We describe the set of all invariant measures on the spaces of universal countable graphs and on the spaces of universal countable triangles-free graphs. The construction uses the description of the S∞-invariant measure on the space of infinite matrices in terms of measurable function of two variables on some special space. In its turn that space is nothing more than the universal continuous (Borel, topological) homogeneous graphs — general or triangle free, — existence of which we establish.
منابع مشابه
Invariant measures on the set of graphs and homogeneous uncountable universal graphs
We describe the set of all invariant measures on the spaces of universal countable graphs and on the spaces of universal countable triangles-free graphs. The construction uses the description of the S∞-invariant measure on the space of infinite matrices in terms of measurable function of two variables on some special space. In its turn that space is nothing more than the universal continuous (B...
متن کاملUncountable graphs and invariant measures on the set of universal countable graphs
We give new examples and describe the complete lists of all measures on the set of countable homogeneous universal graphs and Ksfree homogeneous universal graphs (for s ≥ 3) that are invariant with respect to the group of all permutations of the vertices. Such measures can be regarded as random graphs (respectively, random Ks-free graphs). The well-known example of Erdös–Rényi (ER) of the rando...
متن کاملOn the two-wavelet localization operators on homogeneous spaces with relatively invariant measures
In the present paper, we introduce the two-wavelet localization operator for the square integrable representation of a homogeneous space with respect to a relatively invariant measure. We show that it is a bounded linear operator. We investigate some properties of the two-wavelet localization operator and show that it is a compact operator and is contained in a...
متن کاملRamsey Precompact Expansions of Homogeneous Directed Graphs
In 2005, Kechris, Pestov and Todorčević provided a powerful tool to compute an invariant of topological groups known as the universal minimal flow, immediately leading to an explicit representation of this invariant in many concrete cases. More recently, the framework was generalized allowing for further applications, and the purpose of this paper is to apply these new methods in the context of...
متن کاملOn universal graphs without cliques or without large bipartite graphs
For every uncountable cardinal A, suitable negations of the Generalized Continuum Hypothesis imply: (a) There is no universal Ka 3. The instance Kuf^>t for A = Ni was settled in [KP] from a strengthening of CH.
متن کامل