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)
“If, then, we would indeed restore mankind ... let us first be as simple and well as Nature ourselves, dispel the clouds which hang over our own brows, and take up a little life into our pores. Do not stay to be an overseer of the poor, but endeavor to become one of the worthies of the world.”
—Henry David Thoreau (1817–1862)
“Those things which now most engage the attention of men, as politics and the daily routine, are, it is true, vital functions of human society, but should be unconsciously performed, like the corresponding functions of the physical body.”
—Henry David Thoreau (1817–1862)