mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable...
30 KB (5,339 words) - 13:11, 26 March 2024
p ( σ 2 ∣ ν 0 , σ 0 2 ) = ( σ 0 2 ν 0 2 ) ν 0 / 2 Γ ( ν 0 2 ) exp [ − ν 0 σ 0 2 2 σ 2 ] ( σ 2 ) 1 + ν 0 2 ∝ exp [ − ν 0 σ 0 2 2 σ 2 ] ( σ 2 ) 1...
149 KB (22,391 words) - 14:14, 8 August 2024
σ ) = φ ( ln x − μ σ ) d d x ( ln x − μ σ ) = φ ( ln x − μ σ ) 1 σ x = 1 x σ 2 π exp ( − ( ln x − μ ) 2 2 σ 2...
71 KB (9,576 words) - 13:28, 5 August 2024
Sigma (disambiguation) (redirect from Σ (disambiguation))
Look up sigma, Sigma, Σ, σ, or ς in Wiktionary, the free dictionary. Sigma (Σ or σ, word-final lowercase ς) is the 18th letter of the Greek alphabet. Sigma...
5 KB (630 words) - 14:35, 24 June 2024
is said to be σ-compact if it is the union of countably many compact subspaces. A space is said to be σ-locally compact if it is both σ-compact and (weakly)...
4 KB (536 words) - 21:16, 7 November 2022
anticommutator gives [ σ j , σ k ] + { σ j , σ k } = ( σ j σ k − σ k σ j ) + ( σ j σ k + σ k σ j ) 2 i ε j k ℓ σ ℓ + 2 δ j k I = 2 σ j σ k {\displaystyle...
44 KB (7,416 words) - 16:25, 12 July 2024
defined on a σ-algebra Σ of subsets of a set X is called a finite measure if μ(X) is a finite real number (rather than ∞). A set A in Σ is of finite measure...
9 KB (1,423 words) - 21:07, 11 June 2024
measure theory and functional analysis — the cylindrical σ-algebra or product σ-algebra is a type of σ-algebra which is often used when studying product measures...
2 KB (244 words) - 18:18, 25 May 2024
] = 3 σ i i 2 E [ X i 3 X j ] = 3 σ i i σ i j E [ X i 2 X j 2 ] = σ i i σ j j + 2 σ i j 2 E [ X i 2 X j X k ] = σ i i σ j k + 2 σ i j σ i k E ...
65 KB (9,511 words) - 11:03, 12 July 2024