How to prove that the Modified Boole Transformation preserves the following measure?
$begingroup$
Operator Theoretic Aspects of Ergodic Theory. T. Eisner. B. Farkas. M. Haase and R. Nagel. Page 90 Exercise 3.
How to prove that the following transformation $$T:mathbb{R}rightarrow mathbb{R}$$
$$T(x)=frac{1}{2}left(x-frac{1}{x}right) : xin mathbb{R-{0}}$$ $$T(0)=0$$ preserves the following measure $$lambdaleft([a,b]right)=int_{a}^{b}frac{dx}{pi(1+x^2)}$$
probability-theory measure-theory proof-verification proof-writing ergodic-theory
asked Dec 13 '18 at 3:58
Neil hawkingNeil hawking
1
$endgroup$
add a comment |
$begingroup$
Operator Theoretic Aspects of Ergodic Theory. T. Eisner. B. Farkas. M. Haase and R. Nagel. Page 90 Exercise 3.
How to prove that the following transformation $$T:mathbb{R}rightarrow mathbb{R}$$
$$T(x)=frac{1}{2}left(x-frac{1}{x}right) : xin mathbb{R-{0}}$$ $$T(0)=0$$ preserves the following measure $$lambdaleft([a,b]right)=int_{a}^{b}frac{dx}{pi(1+x^2)}$$
probability-theory measure-theory proof-verification proof-writing ergodic-theory
asked Dec 13 '18 at 3:58
Neil hawkingNeil hawking
1
$endgroup$
add a comment |
$begingroup$
Operator Theoretic Aspects of Ergodic Theory. T. Eisner. B. Farkas. M. Haase and R. Nagel. Page 90 Exercise 3.
How to prove that the following transformation $$T:mathbb{R}rightarrow mathbb{R}$$
$$T(x)=frac{1}{2}left(x-frac{1}{x}right) : xin mathbb{R-{0}}$$ $$T(0)=0$$ preserves the following measure $$lambdaleft([a,b]right)=int_{a}^{b}frac{dx}{pi(1+x^2)}$$
probability-theory measure-theory proof-verification proof-writing ergodic-theory
asked Dec 13 '18 at 3:58
Neil hawkingNeil hawking
1
$endgroup$
Operator Theoretic Aspects of Ergodic Theory. T. Eisner. B. Farkas. M. Haase and R. Nagel. Page 90 Exercise 3.
How to prove that the following transformation $$T:mathbb{R}rightarrow mathbb{R}$$
$$T(x)=frac{1}{2}left(x-frac{1}{x}right) : xin mathbb{R-{0}}$$ $$T(0)=0$$ preserves the following measure $$lambdaleft([a,b]right)=int_{a}^{b}frac{dx}{pi(1+x^2)}$$
probability-theory measure-theory proof-verification proof-writing ergodic-theory
probability-theory measure-theory proof-verification proof-writing ergodic-theory
asked Dec 13 '18 at 3:58
Neil hawkingNeil hawking
1
asked Dec 13 '18 at 3:58
Neil hawkingNeil hawking
1
edited Dec 19 '18 at 8:40
Neil hawking
asked Dec 13 '18 at 3:58
Neil hawkingNeil hawking
1
asked Dec 13 '18 at 3:58
Neil hawkingNeil hawking
1
asked Dec 13 '18 at 3:58
Neil hawkingNeil hawking
1
1
add a comment |
add a comment |
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