All those objects start with axioms and builds up. You can obviously just make simple examples with finite sets. Create the sigma algebra for a dice roll, figure out what a probability really is.
I need a 'Measure Theory for Complete r-tards' book
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All those objects start with axioms and builds up. You can obviously just make simple examples with finite sets. Create the sigma algebra for a dice roll, figure out what a probability really is.
Thank you for the reply. I don't think I'm gonna do econometrics (at least theoretical econometrics), but I need the basics anyway.
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When we talk about the length of a line segment, or the area of a polygon, or the volume that a 3D object fills, we are talking about some notions of the “size” of a region.
Can we formalize this notion, in order to talk about it more precisely?
As it turns out, yes. Measure theory is this formalization.
Measure theory is nothing other than a specification of what we mean when we say a region in space has a size, and of some constraints on the sizes of the unions and intersections of such regions.
If you struggle to understand the above, you may be overthinking it and expecting it to be more complicated than it is.
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You dont need measure theory to understand SDEs etc.
Evans has a book that develops everything needed in ECON without measure theory.Evans is good enough only to have some understanding of what you read. But definitely not good enough if you want to do rigorous research using stochastic calculus.
Saying that, it is also true that many economists who use continuous time have little understanding of technicalities, and that's why there are plenty of papers that include incorrect results, or claims that might be correct but the proofs are incomplete.
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You dont need measure theory to understand SDEs etc.
Evans has a book that develops everything needed in ECON without measure theory.Evans is good enough only to have some understanding of what you read. But definitely not good enough if you want to do rigorous research using stochastic calculus.
Saying that, it is also true that many economists who use continuous time have little understanding of technicalities, and that's why there are plenty of papers that include incorrect results, or claims that might be correct but the proofs are incomplete.Are those technicalities really crucial ?
I doubt.Measure theory is much like rest of real analysis: the critical parts only show in pathological instances, and rest is common sense.
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It depends where you define the cut-off for returds.That is a very good book, but it is also not an easy book, and nowhere near the "measure theory for t-tard's" book that OP is seeking.
1. I’ve heard good things about this book https://www.amazon.com/Theoretic-Probability-Statistical-Probabilistic-Mathematics-ebook/dp/B00INYGDTW
2. Shreve 2 was my first intro to MT as a finance quant, or introduces MT with an eye on stoch calc models in finance. Written for a relatively unsophisticated audience.
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You're clueless
You dont need measure theory to understand SDEs etc.
Evans has a book that develops everything needed in ECON without measure theory.Evans is good enough only to have some understanding of what you read. But definitely not good enough if you want to do rigorous research using stochastic calculus.
Saying that, it is also true that many economists who use continuous time have little understanding of technicalities, and that's why there are plenty of papers that include incorrect results, or claims that might be correct but the proofs are incomplete.Are those technicalities really crucial ?
I doubt.
Measure theory is much like rest of real analysis: the critical parts only show in pathological instances, and rest is common sense. -
All those objects start with axioms and builds up.
That’s a bad way to learn the subject. You’d have no idea why these axioms are the way they are. You need to start from an integral and work your way backwards to discover these axioms for yourself. Then you see why they are inevitable and completely natural, and that there’s really no mystery in measure theory — you could have invented it if Lebesgue didn’t.
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Lol
All those objects start with axioms and builds up.
That’s a bad way to learn the subject. You’d have no idea why these axioms are the way they are. You need to start from an integral and work your way backwards to discover these axioms for yourself. Then you see why they are inevitable and completely natural, and that there’s really no mystery in measure theory — you could have invented it if Lebesgue didn’t.
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You dont need measure theory to understand SDEs etc.
Evans has a book that develops everything needed in ECON without measure theory.Evans is good enough only to have some understanding of what you read. But definitely not good enough if you want to do rigorous research using stochastic calculus.
Saying that, it is also true that many economists who use continuous time have little understanding of technicalities, and that's why there are plenty of papers that include incorrect results, or claims that might be correct but the proofs are incomplete.Are those technicalities really crucial ?
I doubt.
Measure theory is much like rest of real analysis: the critical parts only show in pathological instances, and rest is common sense.Yes, in continuous time those technicalities are crucial.
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All those objects start with axioms and builds up.
That’s a bad way to learn the subject. You’d have no idea why these axioms are the way they are. You need to start from an integral and work your way backwards to discover these axioms for yourself. Then you see why they are inevitable and completely natural, and that there’s really no mystery in measure theory — you could have invented it if Lebesgue didn’t.
Uhh what? Do not do this.
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That is a very good book, but it is also not an easy book, and nowhere near the "measure theory for t-tard's" book that OP is seeking.
1. I’ve heard good things about this book https://www.amazon.com/Theoretic-Probability-Statistical-Probabilistic-Mathematics-ebook/dp/B00INYGDTW
2. Shreve 2 was my first intro to MT as a finance quant, or introduces MT with an eye on stoch calc models in finance. Written for a relatively unsophisticated audience.It depends where you define the cut-off for returds.
Well, I'm assuming that OP is using some standard intro measure theory text. So one can assume he is looking for something substantially easier that such a standard intro.
Also, he did say "measure theory", and not a "measure theoretic introduction to probability".
Pollard is a very good introduction to measure theoretic probability, though it takes a nonstandard approach, and isn't any easier than any of the well known standard intros to measure theory.