Nuprl Lemma : Markov-inequality
∀[p:FinProbSpace]. ∀[n:ℕ]. ∀[X:RandomVariable(p;n)]. ∀[e:ℚ]. E(n;e ≤ X) ≤ (E(n;X)/e) supposing 0 < e supposing 0 ≤ X
Proof
Definitions occuring in Statement :
rv-le: X ≤ Y,
expectation: E(n;F),
rv-const: a,
rv-qle: A ≤ B,
random-variable: RandomVariable(p;n),
finite-prob-space: FinProbSpace,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
qdiv: (r/s),
rationals: ℚ
Lemmas :
rationals_wf,
qdiv_wf,
expectation_wf,
Error :qless_transitivity_2_qorder,
int-subtype-rationals,
Error :qle_weakening_eq_qorder,
Error :qless_irreflexivity,
equal-wf-T-base,
expectation-rv-scale,
iff_weakening_equal,
expectation-monotone,
rv-scale_wf,
Error :qle_wf,
assert-qeq,
assert_wf,
qeq_wf2,
not_wf,
qmul_wf,
qinv_wf,
Error :qmul_assoc_qrng,
Error :qmul_one_qrng,
Error :qmul_comm_qrng,
Error :qinv-positive,
int_seg_wf,
p-outcome_wf,
q_le_wf,
bool_wf,
Error :qmul_preserves_qle,
bnot_wf,
uiff_transitivity2,
eqtt_to_assert,
Error :assert-q_le-eq,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
squash_wf,
true_wf,
Error :qmul_ac_1_qrng,
Error :qmul-qdiv-cancel,
Error :qmul_zero_qrng
\mforall{}[p:FinProbSpace]. \mforall{}[n:\mBbbN{}]. \mforall{}[X:RandomVariable(p;n)].
\mforall{}[e:\mBbbQ{}]. E(n;e \mleq{} X) \mleq{} (E(n;X)/e) supposing 0 < e supposing 0 \mleq{} X
Date html generated:
2015_07_17-AM-07_59_48
Last ObjectModification:
2015_02_03-PM-09_44_47
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