Exactly. I took measure theory in year 3 of my Masters and probability theory in year 4. These types of pure maths courses are very non-intuitive and are very difficult to understand without a decent amount of university level pure maths exposure.

This is all well and fine, and somewhat interesting. But let's not lose sight of the fact that we're talking about poker. Measure theory doesn't apply. Basic probability and game theory is all that's required. Post graduate math courses are overkill. Mason commented on Negreanu's lack of understanding of basic statistics and probability required to understand poker, in his opinion. He may not have been accurate in the universe as a whole with respect to 0 and 1 probabilities, but was accurate for the universe that is poker. Is "almost surely" even mentioned in undergraduate probability courses? Statistics being Mason's area of expertise, statistically speaking, aren't "almost surely" and "surely" equivalent (keep in mind, one of you math guys claimed .999... and 1 were equivalent).

Hi George:

My degrees are in math even though I took extra statistics courses and have always worked in the area of mathematical statistics. However, when in graduate school, I did take a course in measure theory, school year 1974 - 1975, but remember very little from it.

However, I do remember a little, and to give someone reading here an idea of what it does, the (Lebesgue) measure of all the rational numbers from 0 to 1 would be zero and the (Lebesgue) measure of the irrational numbers from 0 to 1 would be 1. And what this means is that using these methods intergration can be done where the standard Riemann integration is not applicable.

However, in poker, and all the other stuff we deal with on a day to day basis, none of this applies.

Best wishes,
Mason

How would you know if measure theory applies if you know nothing about it?
0.999.. and 1 are equivalent.

Please gently remove your head from your ass.

....I feel really dumb lol. Nice play!

you are giving me second hand embarrassment

Likewise.

Ok I stand corrected.

Over an infinite series of poker hands, I'm sure in one of them you'll draw a card from a deck and it will spontaneously combust into nothingness.

Yes as I mentioned several pages ago in day-to-day uses of probability (i.e. from finite state spaces) almost surely and surely are the same thing so the 0 and 1 probability things you were talking about hold true. Statistics and probability are also different things. You could have a degree in statistics and you will be thought of as an applied mathematician and may never come across measure theory or general stochastic processes. Almost surely may be mentioned in an undergrad course depending on if you take the right modules. If you chose to go down the pure route of a general maths degree you will take measure theory as an undergrad and you could also take probability theory as an undergrad although I took it in my Masters year. You will hear about almost everywhere in measure theory and almost surely in probability theory or a course like Markov processes or stochastic calculus. These are the same concept but almost surely makes more sense when talking about probabilities instead of the more general almost everywhere when applied to a general measure.

Also for the .9999...=1 I would think you could just write the LHS an infinite geometric sum with ratio 1/10 and get the result use the infinite geometric sum formula.

having only read the last page, and while likely being less educated and less intelligent than the people arguing I just want to say

heehaww wins