KUSH

139 reputation

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Student taking

Analysis (Lebesque measure, Lebesque integration)
Modern Algebra (Galois theory, etc)

I also teach

Calculus
Elementary number systems

	139 reputation	bio	website		visits	member for	6 months
6 badges		location			seen	Feb 6 at 3:51

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Dec 4	accepted	Real valued function of two variables defined on a square with area one, Partial derivatives exist and bounded by an Lebesque intergrable function
Dec 4	comment	Real valued function of two variables defined on a square with area one, Partial derivatives exist and bounded by an Lebesque intergrable function Indeed. Thanks a bunch!
Dec 4	comment	Real valued function of two variables defined on a square with area one, Partial derivatives exist and bounded by an Lebesque intergrable function Ahh, I think that this should work, $\lim_{n\rightarrow \infty} \frac {f(y+1/n)-f(y)}{1/n} = f'(y)$ for almost every y.
Dec 4	comment	Real valued function of two variables defined on a square with area one, Partial derivatives exist and bounded by an Lebesque intergrable function I'm now trying to think about the sequence of functions assumed in the Lebesque DCT's assumptions. I suppose the Newton quotient would be the converging sequence?
Dec 4	comment	Real valued function of two variables defined on a square with area one, Partial derivatives exist and bounded by an Lebesque intergrable function I didn't think to examine $\frac {d} {dy}$ as a Newton quotient. Given that $\frac {\partial f} {\partial y}$ is dominated by $g$, the Dominated Convergence theorem would be my initial guess (and since the results states the limit movement outright).
Dec 4	accepted	Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products
Dec 4	comment	Real valued function of two variables defined on a square with area one, Partial derivatives exist and bounded by an Lebesque intergrable function I think the Integral Comparison Test might be useful. Assume $f$ measurable, assume there is a nonnegative function dominated by an integrable function $g$ i.e. $\|f\|\le g$ on $E$. Then $\|\int_E f\| \le \int_E \|f\|$
Dec 4	comment	Real valued function of two variables defined on a square with area one, Partial derivatives exist and bounded by an Lebesque intergrable function Theorems from this section: (1) Lebesque Dominated Convergence Theorem. (2) General Lebesque Dominated Convergence Theorem. (3) Integral Comparison Test (4) MCT (5) Fatou's Lemma.
Dec 4	asked	Real valued function of two variables defined on a square with area one, Partial derivatives exist and bounded by an Lebesque intergrable function
Nov 28	revised	Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products deleted 476 characters in body
Nov 28	revised	Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products added 140 characters in body
Nov 28	revised	Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products edited tags
Nov 28	revised	Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products added 23 characters in body
Nov 28	revised	Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products added 108 characters in body
Nov 28	revised	Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products added 439 characters in body
Nov 28	answered	Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products
Nov 28	revised	Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products added 58 characters in body
Nov 28	comment	Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products As in the orbit/stabilizer theorem
Nov 28	comment	Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products $G = stab(e_1) \le GL_n(F)$
Nov 28	asked	Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products