The path integral itself also deals with larger mathematical spaces than is usual, which requires more careful mathematics not all of which has been fully worked out.
12.
Einstein thought that a complete description of physical reality should refer directly to physical space and time, as distinct from the wave function, which refers to an abstract mathematical space.
13.
The terms " stochastic process " and " random process " are used interchangeably, often with no specific mathematical space for the set that indexes the random variables.
14.
It is usually assume that all the random translations have a common probability distribution; hence the displacements form a set of independent and identically distributed random vectors in the underlying mathematical space.
15.
A mathematical model may require randomly moving points of a point process to other locations on the underlying mathematical space, which gives rise to a point process operation known as displacement or translation.
16.
They are necessarily valid of space and all of its phenomenal objects because " a priori " mathematical space is the foundational form of all " a posteriori " external appearance.
17.
In general, the concept of distance is of practical interest for applications, while topological structure is needed for Palm distributions, meaning that point processes are usually defined on mathematical spaces with metrics.
18.
Research published in 2016 by Mathieu Ossendrijver based on tablets found in the British Museum provides evidence that the Babylonians even went so far as to have a concept of objects in an abstract mathematical space.
19.
The function-level approach offers the possibility of making the set of programs a mathematical space by emphasizing the algebraic properties of the program-forming operations over the " space of programs ".
20.
But it has been remarked that the Poisson process does not receive as much attention as it should, partly due to it often being considered just on the real line, and not on other mathematical spaces.
