991 reputation
212
bio website mathtm.blogspot.com
location University of California Los Angeles, CA
age
visits member for 1 year, 11 months
seen Apr 11 at 19:38

I am a recent graduate in applied mathematics at UCLA and currently trying to break into the quantitative investment/trading industry while also continuing to pursue advanced graduate-level mathematics as both a hobby and career necessity.


Oct
28
asked $\ell^{\infty}$ vs. Finite $\ell^{p}$ Norms for Estimating Rates of Convergence of ODE Methods
Oct
21
accepted Clarification on HW Question: Show $inf_{n}P(A_{n})>0$ implies $P(A_{n}\text{i.o.})>0$.
Oct
15
asked Clarification on HW Question: Show $inf_{n}P(A_{n})>0$ implies $P(A_{n}\text{i.o.})>0$.
Sep
9
accepted Limit of Integral of Difference Quotients of Measurable/Bounded $f$ Being $0$ Implies $f$ is Constant
Sep
9
comment Limit of Integral of Difference Quotients of Measurable/Bounded $f$ Being $0$ Implies $f$ is Constant
Can I ask what motivated this proof for you? In other words, what trial and error did you go through before you thought of attacking the problem by defining such $F$?
Sep
8
asked Does Weak $L^{2}$ Convergence on Finite Measure Spaces Imply Strong $L^{1}$ Convergence?
Sep
6
answered Why is compactness so important?
Sep
6
revised Averages of Indicator Functions of Compact Sets in $\mathbb{R}^{2}$ Over Circles
added 136 characters in body
Sep
6
comment Solution to Singular Integral
Are you familiar with contour integration?
Sep
6
revised prove that $(\mathbb{R}^n,\|\cdot\|_\infty)$ is complete.
added 157 characters in body
Sep
6
answered prove that $(\mathbb{R}^n,\|\cdot\|_\infty)$ is complete.
Sep
6
revised Averages of Indicator Functions of Compact Sets in $\mathbb{R}^{2}$ Over Circles
added 660 characters in body
Sep
6
revised Averages of Indicator Functions of Compact Sets in $\mathbb{R}^{2}$ Over Circles
added 316 characters in body
Sep
6
asked Averages of Indicator Functions of Compact Sets in $\mathbb{R}^{2}$ Over Circles
Sep
6
accepted Counter-Example (or Proof) to $\int_{0}^{1}f_{n}\;dx\to0$ Implies $f_{n}\to0$ a.e. $x$ Whenever $f_{n}\geq0$.
Sep
6
revised Limit of Integral of Difference Quotients of Measurable/Bounded $f$ Being $0$ Implies $f$ is Constant
added 97 characters in body
Sep
6
comment Counter-Example (or Proof) to $\int_{0}^{1}f_{n}\;dx\to0$ Implies $f_{n}\to0$ a.e. $x$ Whenever $f_{n}\geq0$.
You're right. I think I need to take a second and rethink, since actually in my comment I really want $\lim nf_{n}$ to converge to $0$ a.e. $x$, not just $f_{n}$.
Sep
6
comment Counter-Example (or Proof) to $\int_{0}^{1}f_{n}\;dx\to0$ Implies $f_{n}\to0$ a.e. $x$ Whenever $f_{n}\geq0$.
Ah. Typewriter sequence. So what if we add the auxiliary condition that $\int_{0}^{1}f_{n}\;dx\to0$ "rapidly" in the sense that $n\int_{0}^{1}f_{n}\;dx\to0$ as $n\to\infty$? Not that the counter-example exploited possible unboundedness of $f_{n}$, but also assume $0\leq f_{n}\leq M$ along with the rapid convergence condition. This is the condition of the convergence in the question I linked in the original post.
Sep
6
revised Counter-Example (or Proof) to $\int_{0}^{1}f_{n}\;dx\to0$ Implies $f_{n}\to0$ a.e. $x$ Whenever $f_{n}\geq0$.
edited title
Sep
6
revised Limit of Integral of Difference Quotients of Measurable/Bounded $f$ Being $0$ Implies $f$ is Constant
added 220 characters in body