Let X = N, E = P(X) and µ be the counting measure on o-algebra E. For each n e N, let An = lim µ(A„). {n,n +1,n + 2,....}. Then show that µ( Ñ An) = n=1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

(in Real Analysis)

Let X = N, E = P(X) and µ be the counting measure on o-algebra E. For each n e N, let
An = {n,n +1,n+ 2,....}. Then show that u( N An)
= lim µ(An).
n=1
Transcribed Image Text:Let X = N, E = P(X) and µ be the counting measure on o-algebra E. For each n e N, let An = {n,n +1,n+ 2,....}. Then show that u( N An) = lim µ(An). n=1
Expert Solution
steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,