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The hypothesis is that, for X is a measure space, f_n(x)->f(x) for each x in X, as n->infty. The hypothesis may be weakened to almost everywhere convergence.

D_P(x)=lim_(epsilon->0)(lnmu(B_epsilon(x)))/(lnepsilon), where B_epsilon(x) is an n-dimensional ball of radius epsilon centered at x and mu is the probability measure.

The power circles of a reference triangle are the three circles centered at the midpoints M_A, M_B, M_C of the sides of a reference triangle DeltaABC that pass through the ...

When a measure lambda is absolutely continuous with respect to a positive measure mu, then it can be written as lambda(E)=int_Efdmu. By analogy with the first fundamental ...

Given a rectangle BCDE, draw EF=DE on an extension of BE. Bisect BF and call the midpoint G. Now draw a semicircle centered at G, and construct the extension of ED which ...

Two links can be continuously deformed into each other iff any diagram of one can be transformed into a diagram of the other by a sequence of Reidemeister moves.

Let f:D(z_0,r)\{z_0}->C be analytic and bounded on a punctured open disk D(z_0,r), then lim_(z->z_0)f(z) exists, and the function defined by f^~:D(z_0,r)->C f^~(z)={f(z) for ...

D = f_(xx)f_(yy)-f_(xy)f_(yx) (1) = f_(xx)f_(yy)-f_(xy)^2, (2) where f_(ij) are partial derivatives.

A set of integers that give the orders of the blocks in a Jordan canonical form, with those integers corresponding to submatrices containing the same latent root bracketed ...

A knot used to shorten a long rope.