Answer to Question #137753 in Real Analysis for Shivam

Question

borel uniqueness theorem

Answer 1

$$SOLUTION$$

From the theory of a Haar measure, is drawn the Borel theorem and some facts whereby the theorem is applied on topological groups.The uniqueness of Borel theorem is vivid under natural conditions for the Borel measure on $E$ . This is considered close to the theory of invariant measures.

Now, using a topological space, $E$ , the collection of subsets $σ-algebra$ can be obtained by a collection of open sets, $E$ known as the Borel $σ-algebra$ of $E$ and is denoted by $B(E)$. Also, The Borel $σ-algebra$ of $R$ is just denoted by $B$.

Nevertheless, a Borel measure on $E$ is the measure of $μ$ on $(E, B(E))$. However, if for all the compact set $K$, $μ(K) < ∞,$ then, $μ$ is known as a Random measure on $E$.