1. In the measurable space (2, B), show A E B iff 1A E B. send HL 2. Let (2, B, P) = ((0, 1], B((0, 1]), A) where λ is Lebesgue measure. De- fine X₁ (w)=0, Vw St. X₂(w) = 1(1/2)(w), X3 (w) = 1Q(w) where QC (0, 1] are the rational numbers in (0, 1]. Note P[X1 = X₂ = X3 = 0] = 1 and give o(X₁), i = 1,2,3.
1. In the measurable space (2, B), show A E B iff 1A E B. send HL 2. Let (2, B, P) = ((0, 1], B((0, 1]), A) where λ is Lebesgue measure. De- fine X₁ (w)=0, Vw St. X₂(w) = 1(1/2)(w), X3 (w) = 1Q(w) where QC (0, 1] are the rational numbers in (0, 1]. Note P[X1 = X₂ = X3 = 0] = 1 and give o(X₁), i = 1,2,3.
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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![3.4 Exercises Solve Exercise 1 & 2 and
1. In the measurable space (2, B), show A E B iff 14 EB. Send them
2. Let (2, B, P) = ((0, 1], B((0, 1]), A) where λ is Lebesgue measure. De-
fine
X₁ (w)=0, VW € S,
X2(w) = 1(1/2)(w),
X3 (w) = 1Q(w)
where QC (0, 1] are the rational numbers in (0, 1). Note
P[X1 X2 X3 = 0] = 1
and give
o(X₁), i 1, 2, 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6344b2d-8fba-4ae4-a76b-36914c334404%2Fe48ff08a-a9fd-4f6e-bc48-10144f4d08bc%2Fyg7cwp4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.4 Exercises Solve Exercise 1 & 2 and
1. In the measurable space (2, B), show A E B iff 14 EB. Send them
2. Let (2, B, P) = ((0, 1], B((0, 1]), A) where λ is Lebesgue measure. De-
fine
X₁ (w)=0, VW € S,
X2(w) = 1(1/2)(w),
X3 (w) = 1Q(w)
where QC (0, 1] are the rational numbers in (0, 1). Note
P[X1 X2 X3 = 0] = 1
and give
o(X₁), i 1, 2, 3.
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