Would anyone be able to throw some light on the convergence of(adsbygoogle = window.adsbygoogle || []).push({});

var[x_t | F_t] , where x_t is a stochastic time-series process, and F_t is the information (it's past history) uptil time t.

What I mean by the question is that

var[x_t | F_t] can be regarded as a function of F_t

say, g(F_t)

Now, does

1/T*g(F_t) ----> converge in probability (a sort of Weak Law of Large Numbers) to its expectation (over the distribution of F_t)?

(possibly under some assumptions on the dependence of F_t through time ?)

Thanks for any help

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# Limit theorem conditioning on information set

Can you offer guidance or do you also need help?

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