Hallo,

How can I show that the algebra generated by a random variable and the algebra generated by and ( is an appropriate measurble function) are equal?

I.e. I want to show

Obviously, it holds that

Can anybody help me?

Thanks in advance.

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- April 30th 2012, 02:58 AMJujusigma-algebra generated by a r.v.
Hallo,

How can I show that the algebra generated by a random variable and the algebra generated by and ( is an appropriate measurble function) are equal?

I.e. I want to show

Obviously, it holds that

Can anybody help me?

Thanks in advance. - April 30th 2012, 03:02 AMgirdavRe: sigma-algebra generated by a r.v.
Show that contains all the elements of the form and , where is measurable.