Radon Measures On Locally Compact Spaces
When the underlying measure space is a locally compact topological space, the definition of a Radon measure can be expressed in terms of continuous linear functionals on the space of continuous functions with compact support. This makes it possible to develop measure and integration in terms of functional analysis, an approach taken by Bourbaki (2004) and a number of other authors.
Read more about this topic: Radon Measure
Famous quotes containing the words measures, locally, compact and/or spaces:
“Him the Almighty Power
Hurld headlong flaming from th’ Ethereal Skie
With hideous ruine and combustion down
To bottomless perdition, there to dwell
In Adamantine Chains and penal Fire,
Who durst defie th’ Omnipotent to Arms.
Nine times the Space that measures Day and Night
To mortal men, he with his horrid crew
Lay vanquisht, rowling in the fiery Gulfe”
—John Milton (1608–1674)
“To see ourselves as others see us can be eye-opening. To see others as sharing a nature with ourselves is the merest decency. But it is from the far more difficult achievement of seeing ourselves amongst others, as a local example of the forms human life has locally taken, a case among cases, a world among worlds, that the largeness of mind, without which objectivity is self- congratulation and tolerance a sham, comes.”
—Clifford Geertz (b. 1926)
“The powers of the federal government ... result from the compact to which the states are parties, [and are] limited by the plain sense and intention of the instrument constituting that compact.”
—James Madison (1751–1836)
“Le silence éternel de ces espaces infinis m’effraie. The eternal silence of these infinite spaces frightens me.”
—Blaise Pascal (1623–1662)