Q4. (a) Let > be a o- 0– Algebra on X. Assume that µ1; H2 : )- [0, 0) are two measures on X. Is µ1 + kµ, a measure on X? where k is a scalar. Consider the cases: k >0 and k < 0. (b) Let (X, > ,4) be a measure space. For A , BE ). Show that u(AUB) = µ(A)+ µ(B) – µ(AN B).
Q4. (a) Let > be a o- 0– Algebra on X. Assume that µ1; H2 : )- [0, 0) are two measures on X. Is µ1 + kµ, a measure on X? where k is a scalar. Consider the cases: k >0 and k < 0. (b) Let (X, > ,4) be a measure space. For A , BE ). Show that u(AUB) = µ(A)+ µ(B) – µ(AN B).
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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Transcribed Image Text:Q4.
(a) Let > be a o- Algebra on X.
Assume that 41, H2 :)- [0, ∞) are two measures on X.
Σ
Is 1 + kfµ, a measure on X? where k is a scalar.
Consider the cases: k >0 and k < 0.
(b) Let (X, >,) be a measure space. For A , Be ).
Show that u(A U B) = µ(A) + µ(B) – µ(An B).
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