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Characteristic Function
Could you please help me with the following problem. If E(exp(i*u*X)) = E(exp(i*u*X)/ G) where G is a sigma algebra and X a random variable then X is independent of G. In the case of two random variables it can be done using inverse Fourier transforms. Is it possible to adapt that method ?Thanks in advance.
Characteristic Function
Not every sigma algebra is generated by a sequence of random variables or am I wrong about this.
Characteristic Function
We solved it. We had to use the fact that if the Fourier Transform is zero then the function is zero a.s. .