Examples
- Every uniformly convergent sequence of bounded functions is uniformly bounded.
- The family of functions defined for real with traveling through the integers, is uniformly bounded by 1.
- The family of derivatives of the above family, is not uniformly bounded. Each is bounded by but there is no real number such that for all integers
Read more about this topic: Uniform Boundedness
Famous quotes containing the word examples:
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)