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For every ergodic flow on a nonatomic probability space, there is a measurable set intersecting almost every orbit in a discrete set.

A roll of 10 on a pair of six-sided dice in the game of craps (Gardner 1978, p. 256). The probability of rolling "a big Dick" is 1/12, or 8.333...%.

If F is the Borel sigma-algebra on some topological space, then a measure m:F->R is said to be a Borel measure (or Borel probability measure). For a Borel measure, all ...

For any integers a_i with 1<=a_1<a_2<...<a_k<=n, the proportion of permutations in the symmetric group S_n whose cyclic decompositions contain no cycles of lengths a_1, a_2, ...

A necessary and sufficient condition for a measure which is quasi-invariant under a transformation to be equivalent to an invariant probability measure is that the ...

A measure algebra which has many properties associated with the convolution measure algebra of a group, but no algebraic structure is assumed for the underlying space.

Let a plane figure have area A and perimeter p. Then Q=(4piA)/(p^2)<=1, where Q is known as the isoperimetric quotient. The equation becomes an equality only for a circle.

A primitive subgroup of the symmetric group S_n is equal to either the alternating group A_n or S_n whenever it contains at least one permutation which is a q-cycle for some ...

A roll of 4 on a pair of six-sided dice in the game of craps (Gardner 1978, p. 256). The probability of rolling "a little Joe" is 1/12, or 8.333...%. A roll of "4 the hard ...

The Mann-Whitney test statistic is equivalent to the Wilcoxon test statistic (van der Waerden 1969).