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- 545 bytes (92 words) - 05:55, 12 May 2008
- 12 bytes (1 word) - 17:30, 10 November 2007
- 158 bytes (25 words) - 09:46, 4 September 2009
- Auto-populated based on [[Special:WhatLinksHere/Measurable function]]. Needs checking by a human.617 bytes (78 words) - 18:24, 11 January 2010
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- {{r|Measurable function}}814 bytes (102 words) - 19:54, 11 January 2010
- {{r|Measurable function}}538 bytes (69 words) - 18:24, 11 January 2010
- {{r|Measurable function}}771 bytes (95 words) - 18:24, 11 January 2010
- {{r|Measurable function}}812 bytes (100 words) - 20:22, 11 January 2010
- {{r|Measurable function}}670 bytes (76 words) - 07:31, 16 April 2010
- ...ons on <math>\scriptstyle \mathbb{R}</math> and integration for general ([[measurable function|measurable]]) functions was defined, also in a natural way, in terms of the [[Measurable function]]4 KB (604 words) - 05:50, 12 May 2008
- ...quivalence class]]es of all complex-valued [[Lebesgue measure|Lebesgue]] [[measurable function|measurable]] scalar square integrable functions on <math>\mathbb{R}</math>1 KB (204 words) - 14:38, 4 January 2009
- ...> an arbitrary [[measurable space]]. Then a '''random variable''' is any [[measurable function]] ''X'' mapping <math>(\Omega,\mathcal{F})</math> to <math>(\Omega',\mathca ...thcal{B}(\mathbb{R}))</math> defined by <math>I(x)=x</math> is trivially a measurable function, hence is a random variable.2 KB (383 words) - 17:06, 17 October 2007
- ...h>\mathbb{C}^n</math>-valued) '''random variable''' is defined to be any [[measurable function]] <math>X:(\Omega,\mathcal{F})\rightarrow (\mathbb{C}^n,\mathcal{B}(\mathbb2 KB (393 words) - 06:53, 14 July 2008
- Auto-populated based on [[Special:WhatLinksHere/Measurable function]]. Needs checking by a human.617 bytes (78 words) - 18:24, 11 January 2010
- {{r|Measurable function}}681 bytes (87 words) - 18:24, 11 January 2010
- ...studies the properties of [[sigma algebra|σ-algebras]], measures, [[measurable function]]s and [[integral]]s.14 KB (2,350 words) - 17:37, 10 November 2007
- *f is [[measurable function|measurable]] and f(s) ≥ 0 for all s in <math>\mathbb{R}</math>6 KB (870 words) - 12:20, 15 November 2007
- ...artingale if <math>\scriptstyle X_t</math> is <math>\mathcal{F}_t</math>-[[measurable function|measurable]] for each <math>\scriptstyle t \,\in\, T</math> and it satisfie3 KB (544 words) - 06:40, 6 March 2008
- ...(x_1,x_2,\ldots,x_N)</math> for some real-valued function ''f'' which is [[measurable function|measurable]] (here with respect to the [[Borel set]]s of <math>\scriptstyle9 KB (1,291 words) - 04:36, 27 June 2009
- ...(x_1,x_2,\ldots,x_N)</math> for some real-valued function ''f'' which is [[measurable function|measurable]] (here with respect to the [[Borel set]]s of <math>\scriptstyle15 KB (2,373 words) - 12:26, 20 February 2021
- ...imilarly to the discrete case, <math>E(|Z||g(X))=E(|Z||X)</math> for every measurable function <math>g</math> that is one-to-one on <math>(-1,1).</math>32 KB (5,149 words) - 15:48, 29 June 2009