Properties of Simple Functions
By definition, the sum, difference, and product of two simple functions are again simple functions, and multiplication by constant keeps a simple function simple; hence it follows that the collection of all simple functions on a given measurable space forms a commutative algebra over .
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Famous quotes containing the words properties of, properties, simple and/or functions:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“Meantime the education of the general mind never stops. The reveries of the true and simple are prophetic. What the tender poetic youth dreams, and prays, and paints today, but shuns the ridicule of saying aloud, shall presently be the resolutions of public bodies, then shall be carried as grievance and bill of rights through conflict and war, and then shall be triumphant law and establishment for a hundred years, until it gives place, in turn, to new prayers and pictures.”
—Ralph Waldo Emerson (1803–1882)
“If photography is allowed to stand in for art in some of its functions it will soon supplant or corrupt it completely thanks to the natural support it will find in the stupidity of the multitude. It must return to its real task, which is to be the servant of the sciences and the arts, but the very humble servant, like printing and shorthand which have neither created nor supplanted literature.”
—Charles Baudelaire (1821–1867)