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:
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“The General Order is always to manoeuver in a body and on the attack; to maintain strict but not pettifogging discipline; to keep the troops constantly at the ready; to employ the utmost vigilance on sentry go; to use the bayonet on every possible occasion; and to follow up the enemy remorselessly until he is utterly destroyed.”
—Lazare Carnot (1753–1823)
“However energetically society in general may strive to make all the citizens equal and alike, the personal pride of each individual will always make him try to escape from the common level, and he will form some inequality somewhere to his own profit.”
—Alexis de Tocqueville (1805–1859)