# Taylor

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bio website mathtm.blogspot.com location University of California Los Angeles, CA age member for 1 year, 11 months seen Apr 11 at 19:38 profile views 223

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.

# 325 Actions

 Oct28 asked $\ell^{\infty}$ vs. Finite $\ell^{p}$ Norms for Estimating Rates of Convergence of ODE Methods Oct21 accepted Clarification on HW Question: Show $inf_{n}P(A_{n})>0$ implies $P(A_{n}\text{i.o.})>0$. Oct15 asked Clarification on HW Question: Show $inf_{n}P(A_{n})>0$ implies $P(A_{n}\text{i.o.})>0$. Sep9 accepted Limit of Integral of Difference Quotients of Measurable/Bounded $f$ Being $0$ Implies $f$ is Constant Sep9 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 $F$? Sep8 asked Does Weak $L^{2}$ Convergence on Finite Measure Spaces Imply Strong $L^{1}$ Convergence? Sep6 answered Why is compactness so important? Sep6 revised Averages of Indicator Functions of Compact Sets in $\mathbb{R}^{2}$ Over Circles added 136 characters in body Sep6 comment Solution to Singular Integral Are you familiar with contour integration? Sep6 revised prove that $(\mathbb{R}^n,\|\cdot\|_\infty)$ is complete. added 157 characters in body Sep6 answered prove that $(\mathbb{R}^n,\|\cdot\|_\infty)$ is complete. Sep6 revised Averages of Indicator Functions of Compact Sets in $\mathbb{R}^{2}$ Over Circles added 660 characters in body Sep6 revised Averages of Indicator Functions of Compact Sets in $\mathbb{R}^{2}$ Over Circles added 316 characters in body Sep6 asked Averages of Indicator Functions of Compact Sets in $\mathbb{R}^{2}$ Over Circles Sep6 accepted Counter-Example (or Proof) to $\int_{0}^{1}f_{n}\;dx\to0$ Implies $f_{n}\to0$ a.e. $x$ Whenever $f_{n}\geq0$. Sep6 revised Limit of Integral of Difference Quotients of Measurable/Bounded $f$ Being $0$ Implies $f$ is Constant added 97 characters in body Sep6 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 $f_{n}$. Sep6 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. Sep6 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 Sep6 revised Limit of Integral of Difference Quotients of Measurable/Bounded $f$ Being $0$ Implies $f$ is Constant added 220 characters in body