Page 274 - DMTH401_REAL ANALYSIS

Real Analysis

Notes 21.3 Keyword

Riemann Stieltjes Integrable: Sum of two Riemann Stieltjes integrable functions is also Riemann
Stieltjes integrable.

21.4 Review Questions

1. Calculate if a < b, ò a fda
b
2. Suppose f is a bounded valued function on [a, b] and f2 Î R on [a, b]. Does it follow that
f ÎR on [a, b]?

3. Show that 0ò1 x2dx = 3/5 where a(n) = x3
4. Show that 0ò2 [x]dx = 3/5 where a(x) = x2 = 3.

Answers: Self Assessment

1. integrable 2. integrable

3. f(x) £ k " x E[a,b] 4. c Î [a, b]

21.5 Further Readings

Books Walter Rudin: Principles of Mathematical Analysis (3rd edition), Ch. 2, Ch. 3.
(3.1-3.12), Ch. 6 (6.1 - 6.22), Ch.7(7.1 - 7.27), Ch. 8 (8.1- 8.5, 8.17 - 8.22).
G.F. Simmons: Introduction to Topology and Modern Analysis, Ch. 2(9-13),
Appendix 1, p. 337-338.
Shanti Narayan: A Course of Mathematical Analysis, 4.81-4.86, 9.1-9.9, Ch.10,Ch.14,
Ch.15(15.2, 15.3, 15.4)

T.M. Apostol: Mathematical Analysis, (2nd Edition) 7.30 and 7.31.
S.C. Malik: Mathematical Analysis.
H.L. Royden: Real Analysis, Ch. 3, 4.

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