Excercise 5 (Evaluation of the integral from below). Let d be a positive integer. Consider the Lebesgue dimensional space (Rd, Leb (R), m). Prove that 1 Spa log(1 + (2) d dm(z) = +∞0. You can use the information that m(B(0,r)) = car", where ca is a constant that depends only on the dimension d. (No need to prove this.)
Excercise 5 (Evaluation of the integral from below). Let d be a positive integer. Consider the Lebesgue dimensional space (Rd, Leb (R), m). Prove that 1 Spa log(1 + (2) d dm(z) = +∞0. You can use the information that m(B(0,r)) = car", where ca is a constant that depends only on the dimension d. (No need to prove this.)
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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![Excercise 5 (Evaluation of the integral from below).
Let d be a positive integer. Consider the Lebesgue dimensional space (Rd, Leb (R), m).
Prove that
1
u log(1 + [x]) d dm(z)= +0.
You can use the information that m(B(0,r)) = car", where ca is a constant that
depends only on the dimension d. (No need to prove this.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f69288b-2977-4881-a4f4-9a3f9fc0a417%2F8478888e-1b0d-42a7-8488-e714e6fefacb%2Ff9l37e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Excercise 5 (Evaluation of the integral from below).
Let d be a positive integer. Consider the Lebesgue dimensional space (Rd, Leb (R), m).
Prove that
1
u log(1 + [x]) d dm(z)= +0.
You can use the information that m(B(0,r)) = car", where ca is a constant that
depends only on the dimension d. (No need to prove this.)
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