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The space I(p). Let p = be bounded sequence of strictly positive numbers, so that 0< Pn S sup p, =H <0o. Let I(p) be the set of all sequences x = such that that is, let Kp) = x =Ex." < Define d(x, y)= where M=max(1, H). Show that d is a metric on I(p). %3!

The space I(p). Let p = be bounded sequence of strictly positive numbers, so that 0< Pn S sup p, =H <0o. Let I(p) be the set of all sequences x = such that that is, let Kp) = x =Ex." < Define d(x, y)= where M=max(1, H). Show that d is a metric on I(p). %3!

Advanced Engineering Mathematics
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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The space /(p). Let p= <p,> be bounded sequence of strictly positive numbers, so that 0< Pa S sup p, =H<o00. Let 1(p) be the set of all sequences x= <r,> such that %3D n-1 that is, let Kp) = x =< x, >:Ex,l*. n-l Define d(x, y)=| where M=max(1, H). Show that d is a metric on l(p).
Transcribed Image Text:The space /(p). Let p= <p,> be bounded sequence of strictly positive numbers, so that 0< Pa S sup p, =H<o00. Let 1(p) be the set of all sequences x= <r,> such that %3D n-1 that is, let Kp) = x =< x, >:Ex,l*. n-l Define d(x, y)=| where M=max(1, H). Show that d is a metric on l(p).
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