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visits member for 1 year, 5 months
seen Feb 6 '13 at 3:51

Student taking

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

I also teach

  • Calculus
  • Elementary number systems

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
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Nov
28
revised Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products
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28
revised Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products
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28
revised Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products
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28
revised Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products
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28
revised Interesting Algebra Problem … involves the subgroup of $GL_n(F)$ that stabilizes $e_1$ and semidirect products
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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
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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