Let X = [0,1], λ be the Lebesgue measure on [0,1] and L(X) be the set of Lebesgue sets measurable on [0,1]. The triplet (X, L(x), 2) is the Lebesgue space on [0,1]. Let f(x) be the simple function defined as: f(x) = 2 * + 6*1 (1-1/(x) 1 [0,1) (x) + 5 * 1{1} (x) + 6 * I Where we remember that IA (x) denotes the indicator function on the set A. Calculate the following Lebesgue integral: [ f(x) dx(x) *Please be as clear as posible, legible, and show and explain all the steps in detail. Thank you very much.
Let X = [0,1], λ be the Lebesgue measure on [0,1] and L(X) be the set of Lebesgue sets measurable on [0,1]. The triplet (X, L(x), 2) is the Lebesgue space on [0,1]. Let f(x) be the simple function defined as: f(x) = 2 * + 6*1 (1-1/(x) 1 [0,1) (x) + 5 * 1{1} (x) + 6 * I Where we remember that IA (x) denotes the indicator function on the set A. Calculate the following Lebesgue integral: [ f(x) dx(x) *Please be as clear as posible, legible, and show and explain all the steps in detail. Thank you very much.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let X = [0,1], λ be the Lebesgue measure on [0,1] and L(X) be the set of Lebesgue sets
measurable on [0,1]. The triplet (X, L(x), λ) is the Lebesgue space on [0,1].
Let f(x) be the simple function defined as:
f(x) = 2 *
110,1 (x) + 5 * I(1) (x) + 6 * I:
'{}
Where we remember that I (x) denotes the indicator function on the set A. Calculate the
following Lebesgue integral:
√x
¹1₁1(x)
f(x) dλ(x)
*Please be as clear as posible, legible, and show and explain all the steps in detail. Thank
you very much.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F090fff48-cd1e-47e1-ae72-a34436ae7ec3%2F5192bc86-6865-4b22-b485-17df77c26ee9%2Fyd1ge8g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X = [0,1], λ be the Lebesgue measure on [0,1] and L(X) be the set of Lebesgue sets
measurable on [0,1]. The triplet (X, L(x), λ) is the Lebesgue space on [0,1].
Let f(x) be the simple function defined as:
f(x) = 2 *
110,1 (x) + 5 * I(1) (x) + 6 * I:
'{}
Where we remember that I (x) denotes the indicator function on the set A. Calculate the
following Lebesgue integral:
√x
¹1₁1(x)
f(x) dλ(x)
*Please be as clear as posible, legible, and show and explain all the steps in detail. Thank
you very much.
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