Question

Give an example of a function that satisfy $\int_a^bf'(x)dx < f(b)-f(a)$ in Lebesgue's theorem

score 59 · Answer 1 · 2016-12-09 18:01:57

59

Views

Give an example of a function that satisfy $\int_a^bf'(x)dx < f(b)-f(a)$ in Lebesgue's theorem

Published on 09 Dec 2016 - 18:01

score 123 · Answer 2 · 2016-12-10 13:53:57

123

Views

Convergence with respect to a specific norm implied by convergence in measure

Published on 10 Dec 2016 - 13:53

score 152 · Answer 3 · 2016-12-10 15:59:18

152

Views

Difficult Maximal Function Inequality

Published on 10 Dec 2016 - 15:59

score 120 · Answer 4 · 2016-12-11 07:51:47

120

Views

Show: If $f_n \ge f$ a. e. then $\int_X \liminf_{n \to \infty}{f_n} \: d\mu \le \liminf_{n \to \infty} \int_X{f_n}d\mu$

Published on 11 Dec 2016 - 7:51

score 1.1k · Answer 5 · 2016-12-11 08:55:18

1.1k

Views

Show that for $|f_n| \le g_n$ $\forall n$: $\lim_{n\to \infty} {\int_E g_n } = \int_E g \Rightarrow \lim_{n\to \infty} {\int_E f_n } = \int_E f$

Published on 11 Dec 2016 - 8:55

score 206 · Answer 6 · 2016-12-11 13:40:55

206

Views

Integrating over a subset (Real Analysis)

Published on 11 Dec 2016 - 13:40

score 319 · Answer 7 · 2026-03-31 18:35:33

319

Views

No Unit in the Convolution Semigroup

Published on 31 Mar 2026 - 18:35

score 69 · Answer 8 · 2016-12-12 00:10:26

69

Views

Counterexample to $\int \left(\sum_\limits{k=1}^{\infty} f_k\right) d\mu = \sum_\limits{k=1}^{\infty} \int f_k d {\mu}$

Published on 12 Dec 2016 - 0:10

score 68 · Answer 9 · 2026-04-04 09:36:24

68

Views

Invertibility of the linear operator?

Published on 04 Apr 2026 - 9:36

score 295 · Answer 10 · 2016-12-13 08:02:22

295

Views

Dirichlet integral $\frac{\sin\ x}{x}$ with lebesgue integration

Published on 13 Dec 2016 - 8:02

score 46 · Answer 11 · 2026-03-31 19:17:51

46

Views

Is $h(x)$ $:=$ $-1^{\lfloor x \rfloor} \over {\lfloor x+1 \rfloor}$ Riemann- and Lebesgue-integrable?

Published on 31 Mar 2026 - 19:17

score 50 · Answer 12 · 2026-03-25 20:12:44

50

Views

Show: $f_n \to f, a.e. \Rightarrow F_n(x) := \int_{(-\infty, x]}{f_n d\lambda^1} \to F_0$

Published on 25 Mar 2026 - 20:12

score 119 · Answer 13 · 2016-12-13 22:54:57

119

Views

Example of Differentiable everywhere but not satisfy Second Fundamental Thm of Calculus

Published on 13 Dec 2016 - 22:54

score 54 · Answer 14 · 2026-03-25 20:11:18

54

Views

Show: $\int_{[a,b]}{f d\lambda^d}=0 \:\:\:\:\forall a, b \in \Bbb R ^d \:\:\mathrm{ with }\:\: a \le b\Rightarrow f=0 \:\:\mathrm{ a.e.}$

Published on 25 Mar 2026 - 20:11

score 160 · Answer 15 · 2016-12-14 10:45:44

160

Views

Proving inequality for lebesgue Stieltjes integral.

Published on 14 Dec 2016 - 10:45

List Question

Give an example of a function that satisfy $\int_a^bf'(x)dx < f(b)-f(a)$ in Lebesgue's theorem

Convergence with respect to a specific norm implied by convergence in measure

Difficult Maximal Function Inequality

Show: If $f_n \ge f$ a. e. then $\int_X \liminf_{n \to \infty}{f_n} \: d\mu \le \liminf_{n \to \infty} \int_X{f_n}d\mu$

Show that for $|f_n| \le g_n$ $\forall n$: $\lim_{n\to \infty} {\int_E g_n } = \int_E g \Rightarrow \lim_{n\to \infty} {\int_E f_n } = \int_E f$

Integrating over a subset (Real Analysis)

No Unit in the Convolution Semigroup

Counterexample to $\int \left(\sum_\limits{k=1}^{\infty} f_k\right) d\mu = \sum_\limits{k=1}^{\infty} \int f_k d {\mu}$

Invertibility of the linear operator?

Dirichlet integral $\frac{\sin\ x}{x}$ with lebesgue integration

Is $h(x)$ $:=$ $-1^{\lfloor x \rfloor} \over {\lfloor x+1 \rfloor}$ Riemann- and Lebesgue-integrable?

Show: $f_n \to f, a.e. \Rightarrow F_n(x) := \int_{(-\infty, x]}{f_n d\lambda^1} \to F_0$

Example of Differentiable everywhere but not satisfy Second Fundamental Thm of Calculus

Show: $\int_{[a,b]}{f d\lambda^d}=0 \:\:\:\:\forall a, b \in \Bbb R ^d \:\:\mathrm{ with }\:\: a \le b\Rightarrow f=0 \:\:\mathrm{ a.e.}$

Proving inequality for lebesgue Stieltjes integral.

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