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seen Aug 18 '13 at 19:22

Jan
20
accepted Integral of simple functions in standard and non-standard representation
Jan
20
comment Integral of simple functions in standard and non-standard representation
Thank you; that's exactly what I was looking for. I tried to edit your post but I couldn't because I wanted to change just two characters. The limits of the last and the third from last summation might be wrong.
Jan
19
comment Integral of simple functions in standard and non-standard representation
Yes, it means that it is a non-negative measurable function.
Jan
19
comment Integral of simple functions in standard and non-standard representation
I would like to prove it without using the linearity of the integral, i.e. just by using the definition of the integral of simple functions (see the latest revision of my question). To say it another way, this question is more about sum and set manipulations than about measure theory.
Jan
19
awarded  Editor
Jan
19
revised Integral of simple functions in standard and non-standard representation
added 542 characters in body
Jan
19
comment Integral of simple functions in standard and non-standard representation
We do not need to use the dominated convergence theorem, nor the linearity of the integral. The simple functions I am talking about take just a finite number of real values (i.e. their image is finite).
Jan
19
comment Integral of simple functions in standard and non-standard representation
Yes, I meant what Thomas said.
Jan
19
asked Integral of simple functions in standard and non-standard representation
Jan
18
awarded  Informed
Jan
17
awarded  Supporter
Jan
17
accepted An inequality about sequences in a $\sigma$-algebra
Jan
17
asked An inequality about sequences in a $\sigma$-algebra
Jan
6
accepted Inequalities with $\sin(z)$, $z \in \mathbb{C}$
Jan
6
comment Inequalities with $\sin(z)$, $z \in \mathbb{C}$
@cameron: I thought we were supposed to find something more explicit. Anyway I'll accept your answer, since you took the time to write it.
Jan
4
comment Inequalities with $\sin(z)$, $z \in \mathbb{C}$
@cameron: I have already tried that. I end up with $\sinh^2y\leq\cos^2x$.
Jan
4
asked Inequalities with $\sin(z)$, $z \in \mathbb{C}$
Jan
1
awarded  Scholar
Jan
1
accepted sequence of complex numbers
Jan
1
awarded  Student