measure theory

probability theory

measurable space, measurable locale

measure, measure space

von Neumann algebra

geometric measure theory

probability space

probability distribution

state

in AQFT and operator algebra

GNS construction

Fell's theorem

entropy, relative entropy

information geometry

information metric

Wasserstein metric

thermodynamics

second law of thermodynamics, generalized second law

ergodic theory

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A probability space is a measure space whose measure is a probability distribution: its integral is 1.

expectation value, moment

entropy