Outer measureIn the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. The theory of outer measures was first introduced by Constantin Carathéodory to provide an abstract basis for the theory of measurable sets and countably additive measures.
Stochastic processIn probability theory and related fields, a stochastic (stəˈkæstɪk) or random process is a mathematical object usually defined as a sequence of random variables, where the index of the sequence has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule.
GIS and hydrologyGeographic information systems (GISs) have become a useful and important tool in the field of hydrology to study and manage Earth's water resources. Climate change and greater demands on water resources require a more knowledgeable disposition of arguably one of our most vital resources. Because water in its occurrence varies spatially and temporally throughout the hydrologic cycle, its study using GIS is especially practical.
Apennine MountainsThe Apennines or Apennine Mountains (ˈæpənaɪn; Ἀπέννινα ὄρη or Ἀπέννινον ὄρος; Appenninus or Apenninus Mons – a singular with plural meaning; Appennini appenˈniːni) are a mountain range consisting of parallel smaller chains extending along the length of peninsular Italy. In the northwest they join with the Ligurian Alps at Altare. In the southwest they end at Reggio di Calabria, the coastal city at the tip of the peninsula.
Italian PeninsulaThe Italian Peninsula (Italian: penisola italica or penisola italiana), also known as the Italic Peninsula or the Apennine Peninsula, is a peninsula extending from the southern Alps in the north to the central Mediterranean Sea in the south. It is nicknamed lo Stivale (the Boot). Three smaller peninsulas contribute to this characteristic shape, namely Calabria (the "toe"), Salento (the "heel") and Gargano (the "spur"). The backbone of the Italian Peninsula consists of the Apennine Mountains, from which it takes one of its names.
Hausdorff measureIn mathematics, Hausdorff measure is a generalization of the traditional notions of area and volume to non-integer dimensions, specifically fractals and their Hausdorff dimensions. It is a type of outer measure, named for Felix Hausdorff, that assigns a number in [0,∞] to each set in or, more generally, in any metric space. The zero-dimensional Hausdorff measure is the number of points in the set (if the set is finite) or ∞ if the set is infinite.
United States Geological SurveyThe United States Geological Survey (USGS), founded as the Geological Survey, is an agency of the United States government whose work spans the disciplines of biology, geography, geology, and hydrology. The agency was founded on March 3, 1879, to study the landscape of the United States, its natural resources, and the natural hazards that threaten it. The agency also makes maps of extraterrestrial planets and moons based on data from U.S. space probes.
