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 Jun 2 awarded Popular Question Sep 24 awarded Autobiographer 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