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:
“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 (15331592)
“Row after row with strict impunity
The headstones yield their names to the element,
The wind whirrs without recollection....”
—Allen Tate (18991979)
“The doctrine of equality!... But there exists no more poisonous poison: for it seems to be preached by justice itself, while it is the end of justice.... Equality for equals, inequality for unequalsMthat would be the true voice of justice: and, what follows from it, Never make equal what is unequal.”
—Friedrich Nietzsche (18441900)