I know that for the Lebesgue measure on $\mathbb{R}^n$, it holds that
For $A \subseteq \mathbb{R}^n$, $$m(A + t) = m(A)$$ and
$$ m(\lambda A) = \lambda^n m(A)$$ for $\lambda > 0.$
Is this true in general for any Borel measure?
I know that for the Lebesgue measure on $\mathbb{R}^n$, it holds that
For $A \subseteq \mathbb{R}^n$, $$m(A + t) = m(A)$$ and
$$ m(\lambda A) = \lambda^n m(A)$$ for $\lambda > 0.$
Is this true in general for any Borel measure?
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