Wp/lus/Aisannazirna

En bawk la : Ái

Aisannazirna hi chhiarkawp péng pakhat a ni a, thil thlen theihna ái sànzawng leh thilthleng kahpahzáwng zirna a ni.

Chawhkawp innghahna a nih avangin kan nitin nunah pawimawhna thûk tak a nei a, thilthleng chingchivêt tak takte mümal taka zir chianna hmanraw ṭha berte zinga mi a ni. Kum zabi sawmhnihna Chhûtkawp thil hmuhchhuah ropui berte zinga mi pawh mürfang (atom) leh a aia thil të lehchhawngte chêtze kahpahzia hmuhchhuah hi a ni. Hei hi Quantum Mechanics thuthlung ber leh khawih ber pakhat pawh a ni.

A lo chhuah dàn

Aisanna chhiarkawp dàn hmanga zirna mümal tak hi kum zabi 16-na chhiarkawpmi Gerolamo Cardano-a'n vanneihnaa innghat infiamna zir chian a tumna leh kum zabi 17-na chhiarkawpmi Pierre de Fermat-a leh Blaise Pascal-a te'n chutiang infiamna an zir chianna aṭanga inṭan a ni deuh ber a. Abîk takin Blaise Pascal-a hi Aisannazirna Pa tia koh a ni. Kum 1657 khan Christiaan Huygens-a, Dutch chhiarkawpmi chuan Aisannazirna lehkhabu a chhuah a ni.

Kalphung

Atirah chuan aisannazirnaah hian thilthleng, a zât chhiar leh thlir chian theih (entirnan: pawisa thïr vàwra chéng zât chuanna lam vawr chhuah theihna ái) lam chauh zir ṭhin a ni a, mahsé chhiarkawpa hmasawnna ṭhang zëlin chutiang thil chauh ni lo, chhiarsèn loh thilte pawh zir a lo tiṭül tâ a, tünah chuan chhiarsen leh chhiarsen loh thil zawng zawng pawh huapin zirna pakhat huangah dah tawh a ni.

A chhiarkawp inṭanna

Pawisa thïr hi vawr ta la, a meilam i vawr chhuah theihna ái engtia sang nge? Engtianga nasain nge a lulam i vawr chhuah i rin? Hei hi chhiarkawp kalhmanga zir tur chuan a lu leh meite hian ái a nei tùr a ni a, ái tih chu thil awmze mumal tak nei a ni bawk tùr a ni. I pawisa thïr vàwr dàn a mumala i pawisa thïr a màm ṭhat chuan (a lulam lang tùr bîk emawa duan leh tihsawih a nih lëm loh chuan) a lu leh mei lan theihna beiseina sànzawng a inang reng a. Chü kan beiseina ái atan chuan, a inzât reng a ni tih entirnan zaa 50 (50%) ve ve kan pè a. Chumi awmzia chu, a lu vawr chhuah theihna ái chu 50% a ni, chu chu '%' tih buai ngai lovin a "zâtvè", ${\frac {1}{2}}$ tiin kan ziak a ni. A mei vawr chhuah theihna ái pawh ${\frac {1}{2}}$ bawk a ni.

bawṭawm, a hmai paruk tihlan ṭheuhna

Chutiang bawkin bawṭawm (dinglama a lem saw en la) hmai ruk nei hi kan vàwr chuan, a hmäi I vawr chhuah theihna ái chu ${\frac {1}{6}}$ a ni a, chutinag bawkin hmai dang - hmai II, hmai III, hmai IV, hmai V, hmai VI - te vawr chhuah theihna ái pawh ${\frac {1}{6}}$ ṭheuh a ni.

Hrilhfiahna chhiarkawp

En bawk la : Tehhmun, Tehhmun, Tehkhäwng, Ái

A chunga kah sawifiahna khi chhiarsèn chinah chauh hmantlâk a ni a, dinhmun zawng zawnga hman theih tùr chuan tehhmunzirna hmanga zir a ngai a ni. A hnuaia thuziak hrethiam tùr chuan "Tehhmunzirna" tih en phawt rawh.

$\left(X,{\mathfrak {M}},\mu \right)$ hi Tehhmun lo ni sé, X Tehzawng hi 1 a nih chuan he tehhmun $\left(X,{\mathfrak {M}},\mu \right)$ hi Aisànhmun tiin kan ko. Tichuan ${\mathfrak {M}}$ hi Airamthlá a ni a, $\mu$ hi aitehna a lo ni ta a ni. Tichuan thilthleng engpawh $E\in {\mathfrak {M}}$ lo awm ta se, E ái (emaw, hetah hi chuan, áisanzawng) chu $\mu \left(E\right)$ a lo ni ta a ni.

Thulâkna

• Elstrodt, Jürgen, Maß- und Integrationstheorie, 7. Auflage, Springer Lehrbuch, 2011.
• Parthasarathy, K.R., Probability Measures on Metric Spaces, Probability and Mathematical Statistics, A Series of Monographs and Textbooks, Academic Press, New York and London, 1967.