Question

how to prove this equality $||f||_{L^p}^{p}=p\int_0^{+\infty} \lambda^{p -1}\mu(E^f_\lambda) d\lambda$

score 144 · Answer 1 · 2026-03-27 20:12:53

144

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how to prove this equality $||f||_{L^p}^{p}=p\int_0^{+\infty} \lambda^{p -1}\mu(E^f_\lambda) d\lambda$

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score 73 · Answer 2 · 2026-04-10 20:05:16

73

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score 1.3k · Answer 3 · 2026-04-08 20:12:00

1.3k

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score 84 · Answer 4 · 2015-01-16 15:17:21

84

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score 325 · Answer 5 · 2026-04-08 19:43:35

325

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score 64 · Answer 6 · 2026-04-14 17:31:10

64

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score 2.4k · Answer 7 · 2026-04-07 22:01:13

2.4k

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score 65 · Answer 8 · 2026-04-14 07:31:54

65

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score 139 · Answer 9 · 2015-01-18 14:06:32

139

Views

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score 74 · Answer 10 · 2026-04-14 03:22:23

74

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Published on 14 Apr 2026 - 3:22

score 40 · Answer 11 · 2026-04-13 01:04:35

40

Views

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score 85 · Answer 12 · 2015-01-19 15:51:13

85

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score 41 · Answer 13 · 2026-04-14 03:27:20

41

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score 35 · Answer 14 · 2026-04-14 05:03:56

35

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score 1.1k · Answer 15 · 2026-04-13 06:44:19

1.1k

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Published on 13 Apr 2026 - 6:44

List Question

how to prove this equality $||f||_{L^p}^{p}=p\int_0^{+\infty} \lambda^{p -1}\mu(E^f_\lambda) d\lambda$

Difficult question on integral

The difference between Riemann integrable function and Lebesgue integrable function

Let A be a measurable set in R. Let B be all of it's densed points. is B necessarily open?

Help with a Royden exercise of measure

Prove that $\int_{[c,d]}|f(x,y)|d\mathcal{L}(y)<\infty$ for $\mathcal{L}$-almost all $x\in [a,b]$.

Evaluating Integrals using Lebesgue Integration

Solving this discontinuous integral using Lebesgue

Royden - section 4.2, page 73 - linearity

Show that $\mu$ is absolutely continuous w.r.t. $\mathcal{L}$ and find $\frac{d\mu} {d\mathcal{L}}$

Non-negative Lebesgue Measurable Functions/Determining Measure of a Particular Set

Convergence of $f_n(x) = 2^n \cdot F(2^n (x-a_n))$ with $F(x) = e^{-x^2}$ with different notions of convergence.

Normalization in $L^{p}$ and $L^{q}$

Sequence of continuous functions convergent to $0$ with the integral equal to $1$

Computing with Lebesgue integrals

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