Talk:Hewitt-Savage zero-one law

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The example seems nearly vacuous, since the only way a random variable taking values in [0, ∞) could fail to have strictly positive expectation is for it to be almost surely zero. Michael Hardy 22:51, 21 August 2006 (UTC)

The emphasis of that example, though, isn't the point about the expectation but rather the application to the Hewitt-Savage zero-one law to see that the probability of the random series diverging is either zero or one. I agree that the example is very simple (and is, indeed, the same one as used for Kolmogorov's zero-one law), but that's not necessarily a bad thing. I would welcome a better showcase example for this result. Sullivan.t.j 23:12, 21 August 2006 (UTC)

I have added a comment on the example being rather simple and the distinction between being able to apply a zero-one law and being able to work out which of the two possible values is the correct one. I have also added a similar warning to Kolmogorov's zero-one law. Sullivan.t.j 23:32, 21 August 2006 (UTC)