24. Suppose (S₁, S₁) is a measurable space and suppose T: S₁ S₂ is a mapping into another space S₂. For an index set I, suppose hy: S2 R, yer and define Ç := 6 (hy, γ ε Γ) to be the o-field of subsets of S2 generated by the real valued family {hy, y € I'}, that is, generated by (h¹(B), y = r, B = B(R)). Show TE S₁/9 iff hy o T is a random variable on (S₁, S₁).
24. Suppose (S₁, S₁) is a measurable space and suppose T: S₁ S₂ is a mapping into another space S₂. For an index set I, suppose hy: S2 R, yer and define Ç := 6 (hy, γ ε Γ) to be the o-field of subsets of S2 generated by the real valued family {hy, y € I'}, that is, generated by (h¹(B), y = r, B = B(R)). Show TE S₁/9 iff hy o T is a random variable on (S₁, S₁).
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.2: Integral Domains And Fields
Problem 3E: Consider the set S={[0],[2],[4],[6],[8],[10],[12],[14],[16]}18, with addition and multiplication as...
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![24. Suppose (S1, S₁) is a measurable space and suppose T S₁ S₂ is a
mapping into another space S₂. For an index set I, suppose
hy: S2 R, yer
and define
Ç := σ (hy, γ ε Γ)
to be the o-field of subsets of S2 generated by the real valued family
(hy, y er}, that is, generated by {h¹(B), y er, B e B(R)). Show
TE S₁/9 iff hy o T is a random variable on (S₁, S₁).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F830f9dd5-4df1-4d70-94bf-f4ca6f6d8c88%2F10e30c31-8dda-4fe1-ab80-578e6e23665f%2F1hiwiuf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:24. Suppose (S1, S₁) is a measurable space and suppose T S₁ S₂ is a
mapping into another space S₂. For an index set I, suppose
hy: S2 R, yer
and define
Ç := σ (hy, γ ε Γ)
to be the o-field of subsets of S2 generated by the real valued family
(hy, y er}, that is, generated by {h¹(B), y er, B e B(R)). Show
TE S₁/9 iff hy o T is a random variable on (S₁, S₁).
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