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 .
Read more about this topic: Simple Function
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)
“It is a curious emotion, this certain homesickness I have in mind. With Americans, it is a national trait, as native to us as the rollercoaster or the jukebox. It is no simple longing for the home town or country of our birth. The emotion is Janus-faced: we are torn between a nostalgia for the familiar and an urge for the foreign and strange. As often as not, we are homesick most for the places we have never known.”
—Carson McCullers (1917–1967)
“The English masses are lovable: they are kind, decent, tolerant, practical and not stupid. The tragedy is that there are too many of them, and that they are aimless, having outgrown the servile functions for which they were encouraged to multiply. One day these huge crowds will have to seize power because there will be nothing else for them to do, and yet they neither demand power nor are ready to make use of it; they will learn only to be bored in a new way.”
—Cyril Connolly (1903–1974)