
[數] 可測集
Lebesgue measurable set and the complete and nowhere dense set are two kinds of important set and are the important content in the real variable function.
勒貝格可測集和疏朗完備集是兩類重要集合,是實變函數中的重要内容。
We know the structure way of the one-dimension no-measurable set, in this paper we first define a amicable set using a mapping, then we give a two-dimension non-measurable set.
一維空間的不可測集的構造方法基本相同,本文通過将二維空間裡的點其對應坐标為有理數的劃分方法來确定親和集,進而給出了一個二維的不可測集。
Set up measurable goals, such as increasing CTR by 2% and reducing costs by 5%, then complete the keyword research, write AD creative, and define compelling offers.
制定可測量的目标,例如增加2%的點擊率并減少5%的成本,然後完善關鍵詞研究、讓廣告更有創意、提供更富吸引力的優惠。
Each area has a set of defined and measurable green house gas (GHG) emissions, on which the majority of these organizations tend to focus their resources and energy.
每個領域都有一組已定義并且可測量的溫室氣體(GHG)排放,大部分這些組織的資源和能源都用于這些方面。
Set one easy, specific, measurable goal. There are several keys to setting this crucial goal.
制定一個容易,明确,可以衡量的目标。
在測度論與實分析中,可測集(measurable set)是能夠被賦予明确“大小”或“測度”的集合。這一概念是構建現代積分理論(如勒貝格積分)和概率論的基礎。
“Measurable set”(可測集)是測度論中的核心概念,其定義和性質如下:
在測度論中,一個集合被稱為可測集,當且僅當它屬于某個預先定義的σ-代數(sigma-algebra)。σ-代數是集合的集合,滿足:
測度(measure)則是定義在σ-代數上的函數,賦予每個可測集一個非負實數(或無窮大),并滿足可數可加性:互不相交的可測集的并的測度等于各集合測度之和。
不可測集的存在表明并非所有集合都能被賦予一緻的測度。例如,維塔利集通過将實數軸劃分為等價類構造,若嘗試為其分配長度會導緻矛盾(如違反可加性)。
簡言之,可測集是測度論中能“合理分配大小”的集合,其性質保證了測度的數學一緻性,成為現代分析學與概率論的基石。
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