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Simple question on simple functions: interpreting the sum sign

score 206 · Answer 1 · 2026-03-20 05:13:32

206

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Simple question on simple functions: interpreting the sum sign

Published on 20 Mar 2026 - 5:13

score 1.5k · Answer 2 · 2018-03-15 01:12:57

1.5k

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Evaluating the Limit of the Integral of $(1-x/n)^n$

Published on 15 Mar 2018 - 1:12

score 50 · Answer 3 · 2018-03-15 01:56:06

50

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Show $g(n)$ takes a finite value for every $n$ for the function $g(n) = \int_{\mathbb{R}} f(x) \sin (nx) \, dx$ where $n \in \mathbb{R}$.

Published on 15 Mar 2018 - 1:56

score 183 · Answer 4 · 2018-03-15 06:00:07

183

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A integrable condition for the distance to boundary function

Published on 15 Mar 2018 - 6:00

score 323 · Answer 5 · 2018-03-15 08:07:03

323

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Calculate $\lim\limits_{n\to\infty}\int_\mathbb{R}f_nd\lambda.$

Published on 15 Mar 2018 - 8:07

score 584 · Answer 6 · 2018-03-17 14:33:44

584

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Are piecewise continuous functions locally integrable?

Published on 17 Mar 2018 - 14:33

score 119 · Answer 7 · 2018-03-17 18:24:16

119

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Show that function introduced by varying upper bound in Lebesgue integral is weakly differentiable

Published on 17 Mar 2018 - 18:24

score 105 · Answer 8 · 2018-03-17 21:52:34

$\int^1_0\int^1_0\frac{x^2-y^2}{(x^2+y^2)^{3/4}} \log(4+\sin x)dydx=\int^1_0\int^1_0 \frac{x^2 - y^2}{(x^2 + y^2)^{3/4}}\log(4+\sin x)dxdy$

score 76 · Answer 9 · 2018-03-18 23:42:47

76

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Let $(f_n)$ be a sequence of measurable functions on a metric space.

Published on 18 Mar 2018 - 23:42

score 284 · Answer 10 · 2018-03-20 23:12:12

284

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Find Lebesgue integral of $\int_{R^n}1_S$ using Fubini.

Published on 20 Mar 2018 - 23:12

score 127 · Answer 11 · 2018-03-21 20:32:40

127

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Show that $\lim\limits_{n \to \infty} \int\limits_0^\infty \frac{x^\frac{1}{n}}{(1+\frac{x}{n})^n} = 1$

Published on 21 Mar 2018 - 20:32

score 40 · Answer 12 · 2018-03-22 01:38:10

40

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$\int_0^1 \log f(t)dt \le \int_0^1 \log g(t)dt$ implies $\int_0^1 \log (f(t)+1)dt \le \int_0^1 \log (g(t)+1)dt$?

Published on 22 Mar 2018 - 1:38

score 33 · Answer 13 · 2018-03-22 06:34:43

33

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$\phi_h(x)=\int_{x+h}^{x+h}f(t)dm(t)$ where $f \in \mathcal{L}^1(\mathbb{R}, \mathcal{B}(\mathbb{R}), m)$

Published on 22 Mar 2018 - 6:34

score 1.3k · Answer 14 · 2018-03-22 17:52:31

1.3k

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Improper Riemann Integral and Lebesgue Integral coincide when...

Published on 22 Mar 2018 - 17:52

score 922 · Answer 15 · 2018-03-22 17:56:25

922

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Generalization of Fatou's Lemma Without the Monotone Convergence Theorem?

Published on 22 Mar 2018 - 17:56

List Question

Simple question on simple functions: interpreting the sum sign

Evaluating the Limit of the Integral of $(1-x/n)^n$

Show $g(n)$ takes a finite value for every $n$ for the function $g(n) = \int_{\mathbb{R}} f(x) \sin (nx) \, dx$ where $n \in \mathbb{R}$.

A integrable condition for the distance to boundary function

Calculate $\lim\limits_{n\to\infty}\int_\mathbb{R}f_nd\lambda.$

Are piecewise continuous functions locally integrable?

Show that function introduced by varying upper bound in Lebesgue integral is weakly differentiable

$\int^1_0\int^1_0\frac{x^2-y^2}{(x^2+y^2)^{3/4}} \log(4+\sin x)dydx=\int^1_0\int^1_0 \frac{x^2 - y^2}{(x^2 + y^2)^{3/4}}\log(4+\sin x)dxdy$

Let $(f_n)$ be a sequence of measurable functions on a metric space.

Find Lebesgue integral of $\int_{R^n}1_S$ using Fubini.

Show that $\lim\limits_{n \to \infty} \int\limits_0^\infty \frac{x^\frac{1}{n}}{(1+\frac{x}{n})^n} = 1$

$\int_0^1 \log f(t)dt \le \int_0^1 \log g(t)dt$ implies $\int_0^1 \log (f(t)+1)dt \le \int_0^1 \log (g(t)+1)dt$?

$\phi_h(x)=\int_{x+h}^{x+h}f(t)dm(t)$ where $f \in \mathcal{L}^1(\mathbb{R}, \mathcal{B}(\mathbb{R}), m)$

Improper Riemann Integral and Lebesgue Integral coincide when...

Generalization of Fatou's Lemma Without the Monotone Convergence Theorem?

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