Michael Greinecker
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Registered User
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1d |
awarded | ● Nice Question |
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May 24 |
awarded | ● Self-Learner |
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May 23 |
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Why did Bourbaki ignore the theory of categories? There are much more qualified people to comment here, but if I recall correctly, it was extensively discussed whether to include categories or not. |
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May 23 |
accepted | From universal measurability to measurability |
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May 23 |
answered | From universal measurability to measurability |
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May 13 |
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From universal measurability to measurability Yes, with "finite" replaced by "measurable". Dellarcherie and Meyer do this in this generality. |
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May 13 |
asked | From universal measurability to measurability |
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Apr 21 |
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Regular Borel Measures equivalent definition They are not equivalent. |
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Apr 21 |
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Regular Borel Measures equivalent definition Not all definitions of regular measures are equivalent, so you should be more explicit with what the "standard definition" is. Also, this is not really research mathematics, so you might want to ask this where such questions are appropriat, such as math.stackexchange.com |
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Apr 18 |
answered | Obtaining conditional probabilities as pushforwards of [0,1] |
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Apr 12 |
awarded | ● Popular Question |
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Apr 10 |
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The shortest mathematical paper This should certainly be community wiki. This thread is closely related and gives examples of shorter papers: mathoverflow.net/questions/7330/… |
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Mar 10 |
asked | Can random elements be defined in terms of a measure algebra? |
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Mar 5 |
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Non-constructive existence proofs without AC? I once asked a related question: mathoverflow.net/questions/81082/… |
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Mar 1 |
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Market-clearing price vector in an “aggregate demand system” The problem is essentially equivalent to the Brouwer fixed point theorem (at least without gross substitutes). |
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Feb 24 |
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Infinite product of finitely-additive probability measures Most proofs of the Daniell-Kolmogorov consistency theorem consist of two steps: Showing that a finitely additve measure on the field is induced. Using a regularity argument to show it is sigma-additive. So, there should be lots of proofs you could cite. |
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Feb 24 |
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Infinite product of finitely-additive probability measures And what should a product measure satisfy? Fubini's theorem does not hold for finitely additive probabilities. |
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Feb 24 |
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Infinite product of finitely-additive probability measures On what sets should the product probability be defined? |
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Feb 19 |
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Simple proof of the existence of Nash equilibria for 2-person games? @Rabee He explains how to prove the general result from existence for finite games using narrow convergence. That's not really practical for classroom use, but should convince mathematicians. |
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Feb 12 |
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“Philosophical” meaning of the Yoneda Lemma The link seems to be broken now. |
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Feb 12 |
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Extension of probability measure from a finite algebra to sigma-algebra with countable many generators @Galle They don't have to be. The Dirac measure $\delta_x$ that assigns measure $1$ to events containing $x$ and $0$ to all others is a measure, no matter what $\sigma$-algebra you use. The measure constructed in Ramiros argument is just a positive linear combination of such measures and hence again a measure (well, one has to adap the argument if some atom has infinite measure, but the logic is the same). |
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Feb 12 |
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Simple proof of the existence of Nash equilibria for 2-person games? Here is what seems to amount to a simplified version of the argument that shows how one can prove the Brouwer fixed point theorem from the existence of Nash equilibria in two player games (modulo a limiting compactness argument): theoryclass.wordpress.com/2012/01/05/… |
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Feb 8 |
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Equilibrium of random zero-sum game, Do the players observe the random payoff before or after they made their choices? In the second case, you can just take the expectation $E[u(i,j)]$ as the payoff of $(i,j)$ and reduce the problem to a standard zero-sum game. |
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Feb 7 |
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Can one view the Independent Product in Probability categorially? @Tom Don't worry, it's great that you aggregate all this information. |
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Feb 6 |
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Can one view the Independent Product in Probability categorially? Thank you, this seems to be exactly what I'm looking for! I will wait a bit and check your paper before accepting your answer. |
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Feb 6 |
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Can one view the Independent Product in Probability categorially? Thank you! These are certainly interesting things to explore. I am familiar with the paper by Culbertson and Sturtz: mathoverflow.net/questions/117294/… :-) |
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Feb 5 |
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Can one view the Independent Product in Probability categorially? @Rabee Tourky: My impression is that most of this stuff can be done in terms of Markov kernels. Grabiszewski constructs his type spaces using kernels directly. The projective limit results underlying the Mertens-Zamir type construction of the universal type space as the space of coherent hierarchies can be proven by getting kernels as disintegrations and then applying the Ionescu-Tulcea theorem. The probability-valued functions used by Heifetz and Samet in their construction are equivalent to kernels... |
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Feb 5 |
asked | Can one view the Independent Product in Probability categorially? |
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Feb 4 |
awarded | ● Nice Answer |
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Feb 4 |
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Is there a natural measures on the space of measurable functions? @Tom LaGatta The paper is open acess of the Bulletin of the AMS, so I included the official link. Thank you for telling me! |
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Feb 4 |
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Is there a natural measures on the space of measurable functions? updated link |
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Feb 2 |
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What is your favorite “strange” function? There are different sensible notions of a constant morphism: nlab.mathforge.org/nlab/show/constant+morphism |
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Jan 28 |
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Concise model of modern fiat money and its non-conservation I agree that the usual use of the mathematical-economics tag should be about mathematical questions within a certain model("Are there existence theorems for equilibria in Arrow-Debreu-McKenzie-Nikaido economies that allow for satiation among consumers?"). The same issue has occured with physiscs: mathoverflow.net/questions/80146/… I think the originalquestion becomes natural when the system is portraied in the media as the central bank simply lending money to private banks, which raises the question how they should ever pay it back. |
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Jan 28 |
awarded | ● Nice Answer |
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Jan 27 |
accepted | Concise model of modern fiat money and its non-conservation |
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Jan 27 |
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Concise model of modern fiat money and its non-conservation @Igor (a) Yes. (b) I did not prevent anyone from reading his writings. (c) Whether I'm open-minded or not would only be relevant if you provided an argument instead of simply stating an opinion. If I have offended you, please excuse my tribal behavior. |
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Jan 27 |
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Concise model of modern fiat money and its non-conservation The Fed is essentially independent of the US government, but there is some influence. It is not completely independent, but it is relatively save from politicians trying to influence it for short term gains. You have got the mechanism essentially right. For securities, things get a bit complicated because nominal payments are denoted in units of money. But the principle work with real assets that are not given in nominal terms. Then the price of the asset s essentially independent of the corresponding payment stream. In practice, the Fed does not try to reduce the money supply. |
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Jan 27 |
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Concise model of modern fiat money and its non-conservation The question was for a foral model of how the fed influences the money supply. Whether such model is useful or not is not part of the question. |
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Jan 27 |
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Concise model of modern fiat money and its non-conservation @IgorRivin I think it is amusing to name a guy who managed to write a several hundred page book of nonsequiturs that are supposed to follow logically from a simple concept (they don't) as someone providing a mathematical model that answers OP questions. I do not care what you think is science or the "social dynamics" of economics. |
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Jan 27 |
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Concise model of modern fiat money and its non-conservation How is this answering the question? |
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Jan 27 |
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Concise model of modern fiat money and its non-conservation Btw: A paper that models open market policies explicitely can be found here: artsci.wustl.edu/~swilliam/papers/… I cannot give any guarantees as tot he quality of the paper. |
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Jan 27 |
answered | Concise model of modern fiat money and its non-conservation |
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Jan 27 |
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Concise model of modern fiat money and its non-conservation I want to point out that Murray Rothbard is seen as a crank by most economists and has essentially no influence in academic economics. |
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Jan 26 |
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Majority vote of total orders I think Gil Kalai proved some generalization of this result, but I'm not sure. |
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Jan 11 |
accepted | Topological conditions of Kolmogorov Extension Theorem |
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Jan 11 |
answered | Topological conditions of Kolmogorov Extension Theorem |
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Jan 4 |
awarded | ● Yearling |
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Jan 1 |
awarded | ● Popular Question |
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Dec 27 |
answered | Applications of the Giry monad in probability and statistics |
