-2
Feynman said,
'If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or the atomic fact, or whatev...
In mathematics, a selection principle is a rule asserting
the possibility of obtaining mathematically significant objects by
selecting elements from given sequences of sets. The theory of selection principles
studies these principles and their relations to other mathematical properties.
Selection principles mainly describe covering properties,
measure- and category-theoretic properties, and local properties in
topological spaces, especially functions spaces. Often, the
characterization of a mathematical property using a selection
principle is a nontrivial task leading to new insights on the...
for continues signal (function) we have Bernstein inequality :
$$
|{df(t)}/dt| \le 2AB\pi
$$
where $A=\sup|f(t)|$ and B is Bandwidth f(t), i.e.
if
$$
F(\omega ) = \int\limits_{ - \infty }^\infty {f(t)} {e^{j\omega t}}dt
$$
then
$$
\omega \ge 2\pi\ B \to F(\omega ) = 0
$$
the question is:
...26
