a function is Riemann-Stieltjes integrable if and only if for each ɛ > 0, there exists a partition P such that U (P, fa) – L(P,f,a) < ɛ, (vi) if f € R(a) on [a,b] and if IF[
a function is Riemann-Stieltjes integrable if and only if for each ɛ > 0, there exists a partition P such that U (P, fa) – L(P,f,a) < ɛ, (vi) if f € R(a) on [a,b] and if IF[
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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Prove the statement in the image.
![a function is Riemann-Stieltjes integrable if and only if for each ɛ > 0, there exists
a partition P such that U (P, fa) – L(P,f,a) < ɛ, (vi) if f € R(a) on [a,b] and if
IF[<M, then | S f da|< M ( a(b) – a(a)), (vii) if f e R(a) and g e R(a) on
[a,b], then fg e R(a) on [a,b].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a6de9c0-0dc9-496d-ac04-6f6e122e4a65%2F311542d9-a0db-42fc-9314-814165430b6e%2F8gk07rd_processed.png&w=3840&q=75)
Transcribed Image Text:a function is Riemann-Stieltjes integrable if and only if for each ɛ > 0, there exists
a partition P such that U (P, fa) – L(P,f,a) < ɛ, (vi) if f € R(a) on [a,b] and if
IF[<M, then | S f da|< M ( a(b) – a(a)), (vii) if f e R(a) and g e R(a) on
[a,b], then fg e R(a) on [a,b].
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