Angle of view camera–subject distance to preserve the size of a subject, changing the angle of view can indirectly distort perspective, changing the apparent relative size of the subject and foreground. If the subject image size remains the same, then at any given aperture all lenses, wide angle and long lenses, will give the same depth of field. An example of how lens choice affects angle of view. This table shows the diagonal, horizontal, and vertical angles of view, in degrees, for lenses producing rectilinear images, when used with 36 mm × 24 mm format (that is, 135 film or full-frame 35mm digital
Gibbs measure Lanford, and Ruelle and provided a framework to directly study infinite systems, instead of taking the limit of finite systems. A measure is a Gibbs measure if the conditional probabilities it induces on each finite subsystem satisfy a consistency condition: if all degrees of freedom outside the finite subsystem are frozen, the canonical ensemble for the subsystem subject to these boundary conditions matches the probabilities in the Gibbs measure conditional on the frozen degrees of freedom. The Hammersley–Clifford theorem implies that any probability measure that satisfies a Markov property is a Gibbs measure for an appropriate choice of (locally defined)