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A sample space is usually denoted using set notation, and the possible ordered outcomes, or sample points, [5] are listed as elements in the set. It is common to refer to a sample space by the labels S, Ω, or U (for "universal set"). The elements of a sample space may be numbers, words, letters, or symbols.
For example, one can define a probability space which models the throwing of a die. A probability space consists of three elements: [1] [2] A sample space, , which is the set of all possible outcomes. An event space, which is a set of events, , an event being a set of outcomes in the sample space.
A sample space must be the sample itself since all the sample points constitute a space, the sample or the sample space. The examples in the article here are actually "measurability" or scale space for the relevant experiments. They are not the samples of the experiments.
In probability theory, an event is a subset of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [1] A single outcome may be an element of many different events, [2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [3]
A three-dimensional Euclidean space is a special case of a Euclidean space. In Bourbaki's terms, [2] the species of three-dimensional Euclidean space is richer than the species of Euclidean space. Likewise, the species of compact topological space is richer than the species of topological space. Fig. 3: Example relations between species of spaces
In complex dynamics, the parameter space is the complex plane C = { z = x + y i : x, y ∈ R}, where i 2 = −1. The famous Mandelbrot set is a subset of this parameter space, consisting of the points in the complex plane which give a bounded set of numbers when a particular iterated function is repeatedly applied from that starting point. The ...
A measure space is a basic object of measure theory, a branch of mathematics that studies generalized notions of volumes. It contains an underlying set, the subsets of this set that are feasible for measuring (the σ-algebra) and the method that is used for measuring (the measure). One important example of a measure space is a probability space.
This glossary of chemistry terms is a list of terms and definitions relevant to chemistry, including chemical laws, diagrams and formulae, laboratory tools, glassware, and equipment. Chemistry is a physical science concerned with the composition, structure, and properties of matter , as well as the changes it undergoes during chemical reactions ...