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Beerus
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6 votes
0 answers
111 views

Time-dependent transition probabilities

6 votes
4 answers
159 views

Prove that $\mu_*\leq\mu^*$ where the definition of an inner and outer measure is induced by a measure

6 votes
0 answers
66 views

Questions About Four Definitions of The Upper and Lower Limits of A Sequence

5 votes
1 answer
57 views

Question About Proving The Countable Subadditivity of $\mu^*:\mathcal{P}(\mathbb{R})\to[0,+\infty]$

4 votes
1 answer
67 views

Question About Half-Open Cubes on $\mathbb{R}^d$

4 votes
1 answer
165 views

Prove the (path-) connectedness of the graph of a compact- and convex-valued upper hemi-continuous correspondence.

4 votes
1 answer
96 views

Prove that a function of $n$ variables is concave if and only if the set below its graph in $\mathbb{R}^{\mathbf{n+1}}$ is a convex set.

4 votes
1 answer
190 views

Question about Rudin's PMA, Chapter 2 Exercise 2

4 votes
1 answer
33 views

How to construct a concrete sequence $\{(a_i,b_i]\}$ such that the inequality $\sum_i(F(b_i)-F(a_i)) < \epsilon$ holds for all $\epsilon>0$?

3 votes
2 answers
50 views

Question on The Theorem of Existence and Uniqueness of The Solutions to Sylvester Equations

3 votes
0 answers
46 views

Prove that a Lebesggue outer measure on $\mathbb{R}^d$ is an outer measure which assigns to each $d$-dimensional interval its volume.

3 votes
0 answers
128 views

Question about the equivalence of three versions of Closed Graph Theorem

3 votes
1 answer
36 views

Question About The Remark after Proposition 1.4.11 from Measure Theory by Donold Cohn

3 votes
1 answer
63 views

The restriction of Lebesgue measure to the $\sigma$-algebra of Borel subsets of $\mathbb{R}$ is not complete.

3 votes
1 answer
56 views

Find a $(X,\mathscr{A})$ and finite measures $\mu$ and $\nu$ such that $\mu(X)=\nu(X)$ but $\{A\in\mathscr{A}:\mu(A)=\nu(A)\}$ not a sigma algebra

3 votes
0 answers
64 views

Understanding Proof of Proposition 2.2.5 from Measure Theory by Donald Cohn

3 votes
1 answer
52 views

Question About Function Integrability - Proposition 2.3.10 from Measury Theory by Donald Cohn

2 votes
1 answer
35 views

If the suprema of a decreasing sequence converges or goes to $+\infty$ then there is a subsequence converge to the limit of suprema or $+\infty$

2 votes
1 answer
38 views

Question About Proof of Proposition 2.3.1 in Measure Theory by Donald Cohn

2 votes
2 answers
80 views

If $x, y$ are rationals with $y > 0$ and $x > 1$, then there exists a positive integer $n$ such that $x^n > y$

1 vote
0 answers
79 views

Proof: Let $x$, $y \in Q$, $y > 0$, $x > 1$. Then there is an integer $n$ such that $x^n < y ≤ x^{n+1}$.

1 vote
1 answer
638 views

The Intuition of Non Degenerate Constraint Qualification and Its Application When The Number of Binding Constraints Is More Than That of Variables

1 vote
0 answers
83 views

About Implicit Function Theorem and Lagrange Multipliers

1 vote
0 answers
34 views

Proof of Second Order Conditions for Maximization Problem with Two Variables and One Inequality Constraint

1 vote
1 answer
62 views

Question About Fritz John Theorem and Slater Constraint Qualification

1 vote
1 answer
63 views

Question on the Construction of the Integral in Measure Theory

1 vote
2 answers
37 views

Borel Functions That Are Continuous

1 vote
2 answers
41 views

If $\int_Afd\mu\geq0$ for all $A\in\mathscr{A}$, then $\int f\chi_Ad\mu=0$ for $A=\{x\in X:f(x)<0\}$

1 vote
0 answers
38 views

Proof of Beppo Levi's Theorem [closed]

1 vote
0 answers
41 views

Prove that $(f+g)(x)<t$ ($t\in\mathbb{R}$) holds if and only if there is a rational number $r$ such that $f(x)<r$ and $g(x)<t-r$.