Example 2.8 (1) Let (X, S) be a measurablespace. Let µ: S → R be defined as:µ(A) = The number of the elements of A(counting measure)Then u is measure.(Check)(2) Let (X, S) be a measurable space. Fix a E X→ R is defined as: µ(A) = 1 if a ¤ A,(point mass measure)µ(A) = 0 if a & A. Then µ is measure (Check)μ: S

Answered: Example 2.8 (1) Let (X, S) be a…

Example 2.8 (1) Let (X, S) be a measurable space. Let µ: S → R be defined as: μ(A) = The number of the elements of A (counting measure) Then u is measure.(Check)

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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Question

Example 2.8 (1) Let (X, S) be a measurable
space. Let µ: S → R be defined as:
µ(A) = The number of the elements of A
(counting measure)
Then u is measure.(Check)
(2) Let (X, S) be a measurable space. Fix a E X
→ R is defined as: µ(A) = 1 if a ¤ A,
(point mass measure)
µ(A) = 0 if a & A. Then µ is measure (Check)
μ: S

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