Let (X, M, μ) be a measure space and (Y, 7) be a topological space. Let f: X→Y be a function. Set Ω = {ECY:f¹(E) ≤ M}. Show that is a o-algebra.
Let (X, M, μ) be a measure space and (Y, 7) be a topological space. Let f: X→Y be a function. Set Ω = {ECY:f¹(E) ≤ M}. Show that is a o-algebra.
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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Prove this
Transcribed Image Text:Let (X, M, µ) be a measure space and (Y, 7) be a topological
space. Let f: X→Y be a function. Set
= {ECY: f¹(E) = M}.
Show that is a o-algebra.
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