- #1
gotjrgkr
- 90
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Hi!
While studying a text " A First Course in Real Analysis" by protter, I've been asked to prove a property of riemann stieltjes integral.
The propery is as follows ; Suppose a<c<b. Assume that not both f and g are discontinuous at c. If [itex]\int[/itex]fdg from a to c and [itex]\int[/itex]fdg ffrom c to b exist, then
[itex]\int[/itex]fdg from a to b exists and [itex]\int[/itex]fdg from a to b = [itex]\int[/itex]fdg from a to c +[itex]\int[/itex]fdg from c to b.
This is written in p.317 of the book.
What I want to ask you is if this property is correct or not.
In some books, incorrect theorems are sometimes introduced. So, those things make me to doubt other books, including the above book.
Thank you for reading my long questions.
While studying a text " A First Course in Real Analysis" by protter, I've been asked to prove a property of riemann stieltjes integral.
The propery is as follows ; Suppose a<c<b. Assume that not both f and g are discontinuous at c. If [itex]\int[/itex]fdg from a to c and [itex]\int[/itex]fdg ffrom c to b exist, then
[itex]\int[/itex]fdg from a to b exists and [itex]\int[/itex]fdg from a to b = [itex]\int[/itex]fdg from a to c +[itex]\int[/itex]fdg from c to b.
This is written in p.317 of the book.
What I want to ask you is if this property is correct or not.
In some books, incorrect theorems are sometimes introduced. So, those things make me to doubt other books, including the above book.
Thank you for reading my long questions.