Complex probability measure and Aharonov's weak value

Fractional Probability Measure and Its Properties

Based on recent studies by Guy Jumarie [1] which defines probability density of fractional order and fractional moments by using fractional calculus (fractional derivatives and fractional integration), this study expands the concept of probability density of fractional order by defining the fractional probability measure, which leads to a fractional probability theory parallel to the classical ...

Weak Value and Weak Measurements

The weak value of a variable O is a description of an effective interaction with that variable in the limit of weak coupling. For a pre-and post-selected system described at time t by the two-state vector Φ| |Ψ (see entry Two-State Vector Formalism), the weak value is [1]: O w ≡ Φ|O|Ψ Φ|Ψ. (1) Contrary to classical physics, variables in quantum mechanics might not have definite values at a give...

Measure theory and probability

1 Construction of measures 3 1.

Measure and Probability

Measure and Probability Theory

1 Sigma-Algebra: Describing measurable sets 6 1.1 Families of sets . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1 Semiring of sets . . . . . . . . . . . . . . . . . . . . . . 7 1.1.2 Restricted algebras . . . . . . . . . . . . . . . . . . . . 10 1.1.3 Sigma Algebras . . . . . . . . . . . . . . . . . . . . . . 10 1.1.4 Binary Unions . . . . . . . . . . . . . . . . . . . . . . 12 1.1...