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Simple question on simple functions: interpreting the sum sign

score 210 · Answer 1 · 2026-04-30 13:15:10

210

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Simple question on simple functions: interpreting the sum sign

Published on 30 Apr 2026 - 13:15

score 1.5k · Answer 2 · 2026-04-14 01:13:54

1.5k

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

Published on 14 Apr 2026 - 1:13

score 53 · Answer 3 · 2026-04-15 07:20:25

53

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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 Apr 2026 - 7:20

score 186 · Answer 4 · 2026-04-14 01:08:27

186

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A integrable condition for the distance to boundary function

Published on 14 Apr 2026 - 1:08

score 326 · Answer 5 · 2026-04-15 06:20:54

326

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

Published on 15 Apr 2026 - 6:20

score 587 · Answer 6 · 2026-04-09 22:45:52

587

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Are piecewise continuous functions locally integrable?

Published on 09 Apr 2026 - 22:45

score 123 · Answer 7 · 2026-05-10 12:32:38

123

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

Published on 10 May 2026 - 12:32

score 108 · Answer 8 · 2026-04-17 03:22:20

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

score 78 · Answer 9 · 2026-04-15 21:24:08

78

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

Published on 15 Apr 2026 - 21:24

score 287 · Answer 10 · 2026-04-15 09:11:10

287

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

Published on 15 Apr 2026 - 9:11

score 130 · Answer 11 · 2026-04-15 15:44:15

130

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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 15 Apr 2026 - 15:44

score 43 · Answer 12 · 2026-04-16 16:52:05

43

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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 16 Apr 2026 - 16:52

score 36 · Answer 13 · 2026-04-14 09:10:36

36

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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 14 Apr 2026 - 9:10

score 1.3k · Answer 14 · 2026-04-13 15:48:55

1.3k

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Improper Riemann Integral and Lebesgue Integral coincide when...

Published on 13 Apr 2026 - 15:48

score 924 · Answer 15 · 2026-04-15 06:42:22

924

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

Published on 15 Apr 2026 - 6:42

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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