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1d
comment Relationship between measure theory and real analysis
Well, measure theory generalizes parts of real analysis. It certainly does not generalize the material on point set topology and functional anlysis in Folland's book.
1d
comment Sufficient conditions for monotonicity with probability distributions
But it is always increasing in $n$.
1d
comment Sufficient conditions for monotonicity with probability distributions
The random variables are all nonnegative?
1d
comment Relationship between measure theory and real analysis
''The name "real analysis" is something of an anachronism. Originally applied to the theory of functions of a real variable, it has come to encompass several subjects of a more general and abstract nature that underlie much of modern analysis.''-Folland Where does it say that measure theory generalizes real analysis?!?! Folland writes no such nonsense.
Dec
16
answered A Pasting lemma for measurable functions
Dec
13
comment Study the convergence of $\sum_{n=1}^{\infty}{\prod_{k=1}^{n}{\sin (k)}}$
Please try to be specific when formulating your questions. You can still edit it. Advice for asking questions well can be found at meta.math.stackexchange.com/questions/9959/….
Dec
11
comment What are the suggested prerequisites for topology?
Ask your teacher, no general answer can be given.
Dec
8
awarded  Caucus
Dec
7
comment Alternate proofs for Collatz 1-Cycles
Made int community wiki upon Fred Kline's request.
Dec
6
comment iid sums of zero mean rv drops below zero almost surely
Nothing prevents your random variables from all being identically zero.
Dec
3
answered unbounded class of ordinals not a set
Dec
2
awarded  Nice Answer
Dec
1
comment Is “total boundedness” a topological property?
There is a different between bounded and totally bounded.
Nov
29
awarded  Good Answer
Nov
29
answered Lower and upper semicontinuity of the Cartesian product
Nov
24
comment It is possible to define our intuitive notion for probability in subsets of $[0,1]$
To make the argument completely rigorous, one has to show that the "winning-sets" of Ann and Bob are measurable in the product. This can be done and it actually holds that $2^{\omega_1}\otimes2^{\omega_1}=2^{\omega_1\times\omega_1}$, as shown here.
Nov
24
comment It is possible to define our intuitive notion for probability in subsets of $[0,1]$
@Ilya Here is my favorite argument: Let $\omega_1$ be the first uncountable ordinal. Let Ann and Bob play the game of picking the larger ordinal number from $\omega_1$. Suppose there is a probability measure $\mu$ on $2^{\omega_1}$ that assigns measure $0$ to finite and therefore countable sets. If both play according to $\mu$, we get that for each $x\in\omega_1$, which is countable, Ann chooses a larger number with probability $1$. So by Fubini's theorem, Ann will win with probability $1$. By symmetry, so does Bob, which cannot be...
Oct
27
comment Minimax Theorems V.S. Fixed Point Theorems.
@Elias For the finite dimensional case, there is the nice book Fixed Point Theorems with Applications to Economics and Game Theory by Kim Border.
Sep
30
awarded  Explainer
Sep
26
comment Books for a beginner
@batpigandme I'm not familiar with the instructor's edition.