Examples For Strict Inequality
Equip the space with the Borel σ-algebra and the Lebesgue measure.
- Example for a probability space: Let denote the unit interval. For every natural number define
- Example with uniform convergence: Let denote the set of all real numbers. Define
These sequences converge on pointwise (respectively uniformly) to the zero function (with zero integral), but every has integral one.
Read more about this topic: Fatou's Lemma
Famous quotes containing the words examples, strict and/or inequality:
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“Compassion is frequently a sense of our own misfortunes, in those of other men; it is an ingenious foresight of the disasters that may fall upon us hereafter. We relieve others, that they may return the like when our occasions call for it; and the good offices we do them are, in strict speaking, so many kindnesses done to ourselves beforehand.”
—François, Duc De La Rochefoucauld (1613–1680)
“Nature is unfair? So much the better, inequality is the only bearable thing, the monotony of equality can only lead us to boredom.”
—Francis Picabia (1878–1953)