Furthermore, every bounded function on a closed bounded interval has a Lebesgue integral and there are many functions with a Lebesgue integral that have no Riemann integral.
12.
Since it is defined as convolution with a bounded function, it is a bounded operator on L 2 ( "'T "').
13.
Contents give a good notion of integrating bounded functions on a space but can behave badly when integrating unbounded functions, while measures give a good notion of integrating unbounded functions.
14.
In mathematical analysis, the "'uniform complex-valued bounded functions " f " defined on a set " S " the non-negative number
15.
A powerful property of G-networks is that they are universal approximators for continuous and bounded functions, so that they can be used to approximate quite general input-output behaviours.
16.
This can also be deduced directly because, after passing to Fourier transforms, " H " ? and " H " become multiplication operators by uniformly bounded functions.
17.
A concrete realization of the * homomorphisms in " X " as " K "-biinvariant uniformly bounded functions on " G " is obtained as follows.
18.
Implicit in the definition of a Riemann integral is that the value of the integral is finite since the function must be a bounded function and the integral must be on a closed interval?
19.
The title of his doctoral thesis was " �ber das Koeffizientenproblem der beschr�nkten Funktionen von zwei Ver�nderlichen " ( " On the coefficient problem of the bounded functions of two variables " ).
20.
In particular, any set that is at most countable has Lebesgue measure zero, and thus a bounded function ( on a compact interval ) with only finitely or countably many discontinuities is Riemann integrable.
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