Measure (physics)

The measure in quantum physics is the integration measure used for performing a path integral.

In quantum field theory, one must sum over all possible histories of a system. When summing over possible histories, which may be very similar to each other, one has to decide when two histories are to be considered different, and when they are to be considered the same, in order not to count the same history twice. This decision is coded within the concept of the measure by an observer.

In fact, the possible histories can be deformed continuously, and therefore the sum is in fact an integral, known as path integral.
In the limit where the sum is becoming an integral, the concept of the measure described above is replaced by an integration measure.

See also

Measure

Measure may refer to:

Legal

Mathematics and science

Units

Measure (album)

Measure is the second album from Matt Pond PA, released in 2000.

Track listing

Personnel

Technical personnel

Termination analysis

In computer science, a termination analysis is program analysis which attempts to determine whether the evaluation of a given program will definitely terminate. Because the halting problem is undecidable, termination analysis cannot be total. The aim is to find the answer "program does terminate" (or "program does not terminate") whenever this is possible. Without success the algorithm (or human) working on the termination analysis may answer with "maybe" or continue working infinitely long.

Termination proof

A termination proof is a type of mathematical proof that plays a critical role in formal verification because total correctness of an algorithm depends on termination.

A simple, general method for constructing termination proofs involves associating a measure with each step of an algorithm. The measure is taken from the domain of a well-founded relation, such as from the ordinal numbers. If the measure "decreases" according to the relation along every possible step of the algorithm, it must terminate, because there are no infinite descending chains with respect to a well-founded relation.