Let 1 ≤ p < ∞ and let {fn} be a sequence of functions in Lp[a, b]. Suppose there is a function f ∈ Lp[a, b] with limn→∞ ||fn − f||p = 0 . Prove that {fn} is a Cauchy sequence in Lp[a, b].

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

Let 1 ≤ p < ∞ and let {fn} be a sequence of functions in
Lp[a, b]. Suppose there is a function f ∈ Lp[a, b] with
limn→∞ ||fn − f||p = 0 .
Prove that {fn} is a Cauchy sequence in Lp[a, b].

(16) Let 1 <p<00 and let {Sn} be a sequence of functions in
LP la, 6). Suppose there is a function fe LPla, b] with
lim If.- flp 0.
Prove that {fa} is a Cauchy sequence in LP(a, b).
Transcribed Image Text:(16) Let 1 <p<00 and let {Sn} be a sequence of functions in LP la, 6). Suppose there is a function fe LPla, b] with lim If.- flp 0. Prove that {fa} is a Cauchy sequence in LP(a, b).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 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,