Borel Gspace
A (standard) Borel Gspace is defined in connection with a standard Borel space which shall be specified first.
0.1 Basic definitions

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a. Standard Borel space
Definition 0.1.
A standard Borel space is defined as a measurable space^{}, that is, a set $X$ equipped with a $\sigma $ algebra^{} $\mathcal{S}$, such that there exists a Polish topology^{} on $X$ with $S$ its $\sigma $algebra of Borel sets.

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b. Borel Gspace
Definition 0.2.
Let $G$ be a Polish group and $X$ a (standard) Borel space^{}. An action $a$ of $G$ on $X$ is defined to be a Borel action if $a:G\times X\to X$ is a Borelmeasurable map or a Borel function (http://planetmath.org/BorelGroupoid). In this case, a standard Borel space $X$ that is acted upon by a Polish group with a Borel action is called a (standard) Borel Gspace.

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Definition 0.3.
Homomorphisms^{}, embeddings^{} or isomorphisms^{} between standard Borel Gspaces are called Borel if they are Borel–measurable.
Remark 0.1.
Title  Borel Gspace 
Canonical name  BorelGspace 
Date of creation  20130322 18:24:45 
Last modified on  20130322 18:24:45 
Owner  bci1 (20947) 
Last modified by  bci1 (20947) 
Numerical id  14 
Author  bci1 (20947) 
Entry type  Definition 
Classification  msc 22A15 
Classification  msc 22A25 
Classification  msc 22A22 
Classification  msc 54H05 
Classification  msc 22A05 
Classification  msc 22A10 
Related topic  BorelSpace 
Related topic  BorelMeasure 
Related topic  BorelGroupoid 
Related topic  CategoryOfBorelSpaces 
Defines  Borel action 
Defines  Borelmeasurable map 
Defines  standard Borel space 