enow.com Web Search

Search results

1. Results from the WOW.Com Content Network

2. Lebesgue integral - Wikipedia

   en.wikipedia.org/wiki/Lebesgue_integral

   The Lebesgue integral describes better how and when it is possible to take limits under the integral sign (via the monotone convergence theorem and dominated convergence theorem). While the Riemann integral considers the area under a curve as made out of vertical rectangles, the Lebesgue definition considers horizontal slabs that are not ...

3. Locally integrable function - Wikipedia

   en.wikipedia.org/wiki/Locally_integrable_function

   is not locally integrable in x = 0: it is indeed locally integrable near this point since its integral over every compact set not including it is finite. Formally speaking, 1 / x ∈ L 1 , l o c ( R ∖ 0 ) {\displaystyle 1/x\in L_{1,loc}(\mathbb {R} \setminus 0)} : [ 19 ] however, this function can be extended to a distribution on the whole R ...

4. Lebesgue–Stieltjes integration - Wikipedia

   en.wikipedia.org/wiki/Lebesgue–Stieltjes...

   An alternative approach (Hewitt & Stromberg 1965) is to define the Lebesgue–Stieltjes integral as the Daniell integral that extends the usual Riemann–Stieltjes integral. Let g be a non-decreasing right-continuous function on [ a , b ] , and define I ( f ) to be the Riemann–Stieltjes integral

5. Fatou's lemma - Wikipedia

   en.wikipedia.org/wiki/Fatou's_lemma

   In mathematics, Fatou's lemma establishes an inequality relating the Lebesgue integral of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions. The lemma is named after Pierre Fatou. Fatou's lemma can be used to prove the Fatou–Lebesgue theorem and Lebesgue's dominated convergence theorem.

6. Dominated convergence theorem - Wikipedia

   en.wikipedia.org/wiki/Dominated_convergence_theorem

   Lebesgue's dominated convergence theorem is a special case of the Fatou–Lebesgue theorem. Below, however, is a direct proof that uses Fatou’s lemma as the essential tool. Since f is the pointwise limit of the sequence (f n) of measurable functions that are dominated by g, it is also measurable and dominated by g, hence it is integrable ...

7. Lebesgue integrability - Wikipedia

   en.wikipedia.org/wiki/Lebesgue_integrability

   In mathematics, Lebesgue integrability may refer to: Whether the Lebesgue integral of a function is defined; this is what is most often meant. The Lebesgue integrability condition , which determines whether the Riemann integral of a function is defined.

8. How to watch MLB’s Opening Day for free—and without cable

   www.aol.com/finance/watch-mlb-opening-day-free...

   MLB.tv offers a seven-day free trial, after which you’ll pay $30 per month or $150 for the season. ... Hulu with Live TV. The free trial on this service is no longer offered. It will now cost ...

9. Integration by substitution - Wikipedia

   en.wikipedia.org/wiki/Integration_by_substitution

   For Lebesgue measurable functions, the theorem can be stated in the following form: [6] Theorem — Let U be a measurable subset of R n and φ : U → R n an injective function , and suppose for every x in U there exists φ ′( x ) in R n , n such that φ ( y ) = φ ( x ) + φ′ ( x )( y − x ) + o (‖ y − x ‖) as y → x (here o is ...